diff --git a/deps/v8/src/common/globals.h b/deps/v8/src/common/globals.h
index dbc6b9af9be02a..f75544b56c0e9e 100644
--- a/deps/v8/src/common/globals.h
+++ b/deps/v8/src/common/globals.h
@@ -349,6 +349,9 @@ constexpr int kUC16Size = sizeof(uc16);  // NOLINT
 // 128 bit SIMD value size.
 constexpr int kSimd128Size = 16;
 
+// Maximum ordinal used for tracking asynchronous module evaluation order.
+constexpr unsigned kMaxModuleAsyncEvaluatingOrdinal = (1 << 30) - 1;
+
 // FUNCTION_ADDR(f) gets the address of a C function f.
 #define FUNCTION_ADDR(f) (reinterpret_cast<v8::internal::Address>(f))
 
diff --git a/deps/v8/src/diagnostics/objects-debug.cc b/deps/v8/src/diagnostics/objects-debug.cc
index 054b9dec175fb2..ee8827f8f639f3 100644
--- a/deps/v8/src/diagnostics/objects-debug.cc
+++ b/deps/v8/src/diagnostics/objects-debug.cc
@@ -1390,7 +1390,8 @@ void SourceTextModule::SourceTextModuleVerify(Isolate* isolate) {
           (status() == kPreInstantiating && code().IsSharedFunctionInfo()) ||
           (status() == kUninstantiated && code().IsSharedFunctionInfo()));
     CHECK(top_level_capability().IsUndefined() && !AsyncParentModuleCount() &&
-          !pending_async_dependencies() && !async_evaluating());
+          !pending_async_dependencies());
+    CHECK(!IsAsyncEvaluating());
   }
 
   CHECK_EQ(requested_modules().length(), info().module_requests().length());
diff --git a/deps/v8/src/diagnostics/objects-printer.cc b/deps/v8/src/diagnostics/objects-printer.cc
index 843d65cd1f7f61..9e24b5c41d1997 100644
--- a/deps/v8/src/diagnostics/objects-printer.cc
+++ b/deps/v8/src/diagnostics/objects-printer.cc
@@ -1602,6 +1602,7 @@ void SourceTextModule::SourceTextModulePrint(std::ostream& os) {  // NOLINT
   os << "\n - script: " << Brief(script());
   os << "\n - import_meta: " << Brief(import_meta());
   os << "\n - cycle_root: " << Brief(cycle_root());
+  os << "\n - async_evaluating_ordinal: " << async_evaluating_ordinal();
   os << "\n";
 }
 
diff --git a/deps/v8/src/execution/isolate-inl.h b/deps/v8/src/execution/isolate-inl.h
index b3a84d01bec1e6..e39b75f02508dc 100644
--- a/deps/v8/src/execution/isolate-inl.h
+++ b/deps/v8/src/execution/isolate-inl.h
@@ -13,6 +13,7 @@
 #include "src/objects/property-cell.h"
 #include "src/objects/regexp-match-info.h"
 #include "src/objects/shared-function-info.h"
+#include "src/objects/source-text-module.h"
 
 namespace v8 {
 namespace internal {
@@ -118,6 +119,36 @@ Isolate::ExceptionScope::~ExceptionScope() {
   isolate_->set_pending_exception(*pending_exception_);
 }
 
+void Isolate::DidFinishModuleAsyncEvaluation(unsigned ordinal) {
+  // To address overflow, the ordinal is reset when the async module with the
+  // largest vended ordinal finishes evaluating. Modules are evaluated in
+  // ascending order of their async_evaluating_ordinal.
+  //
+  // While the specification imposes a global total ordering, the intention is
+  // that for each async module, all its parents are totally ordered by when
+  // they first had their [[AsyncEvaluating]] bit set.
+  //
+  // The module with largest vended ordinal finishes evaluating implies that the
+  // async dependency as well as all other modules in that module's graph
+  // depending on async dependencies are finished evaluating.
+  //
+  // If the async dependency participates in other module graphs (e.g. via
+  // dynamic import, or other <script type=module> tags), those module graphs
+  // must have been evaluated either before or after the async dependency is
+  // settled, as the concrete Evaluate() method on cyclic module records is
+  // neither reentrant nor performs microtask checkpoints during its
+  // evaluation. If before, then all modules that depend on the async
+  // dependencies were given an ordinal that ensure they are relatively ordered,
+  // before the global ordinal was reset. If after, then the async evaluating
+  // ordering does not apply, as the dependency is no longer asynchronous.
+  //
+  // https://tc39.es/ecma262/#sec-moduleevaluation
+  if (ordinal + 1 == next_module_async_evaluating_ordinal_) {
+    next_module_async_evaluating_ordinal_ =
+        SourceTextModule::kFirstAsyncEvaluatingOrdinal;
+  }
+}
+
 #define NATIVE_CONTEXT_FIELD_ACCESSOR(index, type, name)    \
   Handle<type> Isolate::name() {                            \
     return Handle<type>(raw_native_context().name(), this); \
diff --git a/deps/v8/src/execution/isolate.cc b/deps/v8/src/execution/isolate.cc
index bd357d4bfc9991..6174c61cb04554 100644
--- a/deps/v8/src/execution/isolate.cc
+++ b/deps/v8/src/execution/isolate.cc
@@ -69,6 +69,7 @@
 #include "src/objects/prototype.h"
 #include "src/objects/slots.h"
 #include "src/objects/smi.h"
+#include "src/objects/source-text-module.h"
 #include "src/objects/stack-frame-info-inl.h"
 #include "src/objects/visitors.h"
 #include "src/profiler/heap-profiler.h"
@@ -2929,6 +2930,8 @@ Isolate::Isolate(std::unique_ptr<i::IsolateAllocator> isolate_allocator)
 #if V8_SFI_HAS_UNIQUE_ID
       next_unique_sfi_id_(0),
 #endif
+      next_module_async_evaluating_ordinal_(
+          SourceTextModule::kFirstAsyncEvaluatingOrdinal),
       cancelable_task_manager_(new CancelableTaskManager()) {
   TRACE_ISOLATE(constructor);
   CheckIsolateLayout();
diff --git a/deps/v8/src/execution/isolate.h b/deps/v8/src/execution/isolate.h
index 8c538ab27de3da..a35ef10cf2eefb 100644
--- a/deps/v8/src/execution/isolate.h
+++ b/deps/v8/src/execution/isolate.h
@@ -1284,6 +1284,22 @@ class V8_EXPORT_PRIVATE Isolate final : private HiddenFactory {
     return id;
   }
 
+  // https://github.com/tc39/proposal-top-level-await/pull/159
+  // TODO(syg): Update to actual spec link once merged.
+  //
+  // According to the spec, modules that depend on async modules (i.e. modules
+  // with top-level await) must be evaluated in order in which their
+  // [[AsyncEvaluating]] flags were set to true. V8 tracks this global total
+  // order with next_module_async_evaluating_ordinal_. Each module that sets its
+  // [[AsyncEvaluating]] to true grabs the next ordinal.
+  unsigned NextModuleAsyncEvaluatingOrdinal() {
+    unsigned ordinal = next_module_async_evaluating_ordinal_++;
+    CHECK_LT(ordinal, kMaxModuleAsyncEvaluatingOrdinal);
+    return ordinal;
+  }
+
+  inline void DidFinishModuleAsyncEvaluation(unsigned ordinal);
+
   void AddNearHeapLimitCallback(v8::NearHeapLimitCallback, void* data);
   void RemoveNearHeapLimitCallback(v8::NearHeapLimitCallback callback,
                                    size_t heap_limit);
@@ -1815,6 +1831,8 @@ class V8_EXPORT_PRIVATE Isolate final : private HiddenFactory {
   std::atomic<int> next_unique_sfi_id_;
 #endif
 
+  unsigned next_module_async_evaluating_ordinal_;
+
   // Vector of callbacks before a Call starts execution.
   std::vector<BeforeCallEnteredCallback> before_call_entered_callbacks_;
 
diff --git a/deps/v8/src/heap/factory.cc b/deps/v8/src/heap/factory.cc
index 22dcb1838a5b0f..de221e22f239b7 100644
--- a/deps/v8/src/heap/factory.cc
+++ b/deps/v8/src/heap/factory.cc
@@ -2504,7 +2504,7 @@ Handle<SourceTextModule> Factory::NewSourceTextModule(
   module->set_top_level_capability(roots.undefined_value());
   module->set_flags(0);
   module->set_async(IsAsyncModule(code->kind()));
-  module->set_async_evaluating(false);
+  module->set_async_evaluating_ordinal(SourceTextModule::kNotAsyncEvaluated);
   module->set_cycle_root(roots.the_hole_value());
   module->set_async_parent_modules(*async_parent_modules);
   module->set_pending_async_dependencies(0);
diff --git a/deps/v8/src/objects/module-inl.h b/deps/v8/src/objects/module-inl.h
index d270a9cdfc3671..2ce37f231f8473 100644
--- a/deps/v8/src/objects/module-inl.h
+++ b/deps/v8/src/objects/module-inl.h
@@ -37,8 +37,8 @@ SMI_ACCESSORS(Module, status, kStatusOffset)
 SMI_ACCESSORS(Module, hash, kHashOffset)
 
 BOOL_ACCESSORS(SourceTextModule, flags, async, AsyncBit::kShift)
-BOOL_ACCESSORS(SourceTextModule, flags, async_evaluating,
-               AsyncEvaluatingBit::kShift)
+BIT_FIELD_ACCESSORS(SourceTextModule, flags, async_evaluating_ordinal,
+                    SourceTextModule::AsyncEvaluatingOrdinalBits)
 ACCESSORS(SourceTextModule, async_parent_modules, ArrayList,
           kAsyncParentModulesOffset)
 ACCESSORS(SourceTextModule, top_level_capability, HeapObject,
@@ -141,6 +141,10 @@ int SourceTextModule::AsyncParentModuleCount() {
   return async_parent_modules().Length();
 }
 
+bool SourceTextModule::IsAsyncEvaluating() const {
+  return async_evaluating_ordinal() >= kFirstAsyncEvaluatingOrdinal;
+}
+
 bool SourceTextModule::HasPendingAsyncDependencies() {
   DCHECK_GE(pending_async_dependencies(), 0);
   return pending_async_dependencies() > 0;
diff --git a/deps/v8/src/objects/source-text-module.cc b/deps/v8/src/objects/source-text-module.cc
index 9000aa1e61bcf8..225636a535d794 100644
--- a/deps/v8/src/objects/source-text-module.cc
+++ b/deps/v8/src/objects/source-text-module.cc
@@ -76,6 +76,15 @@ class Module::ResolveSet
   Zone* zone_;
 };
 
+struct SourceTextModule::AsyncEvaluatingOrdinalCompare {
+  bool operator()(Handle<SourceTextModule> lhs,
+                  Handle<SourceTextModule> rhs) const {
+    DCHECK(lhs->IsAsyncEvaluating());
+    DCHECK(rhs->IsAsyncEvaluating());
+    return lhs->async_evaluating_ordinal() < rhs->async_evaluating_ordinal();
+  }
+};
+
 SharedFunctionInfo SourceTextModule::GetSharedFunctionInfo() const {
   DisallowHeapAllocation no_alloc;
   switch (status()) {
@@ -579,6 +588,58 @@ void SourceTextModule::FetchStarExports(Isolate* isolate,
   module->set_exports(*exports);
 }
 
+void SourceTextModule::GatherAsyncParentCompletions(
+    Isolate* isolate, Zone* zone, Handle<SourceTextModule> start,
+    AsyncParentCompletionSet* exec_list) {
+  // The spec algorithm is recursive. It is transformed to an equivalent
+  // iterative one here.
+  ZoneStack<Handle<SourceTextModule>> worklist(zone);
+  worklist.push(start);
+
+  while (!worklist.empty()) {
+    Handle<SourceTextModule> module = worklist.top();
+    worklist.pop();
+
+    // 1. Assert: module.[[Status]] is evaluated.
+    DCHECK_EQ(module->status(), kEvaluated);
+
+    // 2. For each Module m of module.[[AsyncParentModules]], do
+    for (int i = module->AsyncParentModuleCount(); i-- > 0;) {
+      Handle<SourceTextModule> m = module->GetAsyncParentModule(isolate, i);
+
+      // a. If execList does not contain m and
+      //    m.[[CycleRoot]].[[EvaluationError]] is empty, then
+      if (exec_list->find(m) == exec_list->end() &&
+          m->GetCycleRoot(isolate)->status() != kErrored) {
+        // i. Assert: m.[[EvaluationError]] is empty.
+        DCHECK_NE(m->status(), kErrored);
+
+        // ii. Assert: m.[[AsyncEvaluating]] is true.
+        DCHECK(m->IsAsyncEvaluating());
+
+        // iii. Assert: m.[[PendingAsyncDependencies]] > 0.
+        DCHECK(m->HasPendingAsyncDependencies());
+
+        // iv. Set m.[[PendingAsyncDependencies]] to
+        //     m.[[PendingAsyncDependencies]] - 1.
+        m->DecrementPendingAsyncDependencies();
+
+        // v. If m.[[PendingAsyncDependencies]] is equal to 0, then
+        if (!m->HasPendingAsyncDependencies()) {
+          // 1. Append m to execList.
+          exec_list->insert(m);
+
+          // 2. If m.[[Async]] is false,
+          //    perform ! GatherAsyncParentCompletions(m, execList).
+          if (!m->async()) worklist.push(m);
+        }
+      }
+    }
+  }
+
+  // 3. Return undefined.
+}
+
 Handle<JSModuleNamespace> SourceTextModule::GetModuleNamespace(
     Isolate* isolate, Handle<SourceTextModule> module, int module_request) {
   Handle<Module> requested_module(
@@ -665,7 +726,7 @@ MaybeHandle<Object> SourceTextModule::EvaluateMaybeAsync(
     CHECK_EQ(module->status(), kEvaluated);
 
     //  b. If module.[[AsyncEvaluating]] is false, then
-    if (!module->async_evaluating()) {
+    if (!module->IsAsyncEvaluating()) {
       //   i. Perform ! Call(capability.[[Resolve]], undefined,
       //                     «undefined»).
       JSPromise::Resolve(capability, isolate->factory()->undefined_value())
@@ -718,81 +779,97 @@ MaybeHandle<Object> SourceTextModule::Evaluate(
 
 void SourceTextModule::AsyncModuleExecutionFulfilled(
     Isolate* isolate, Handle<SourceTextModule> module) {
-  // 1. Assert: module.[[Status]] is "evaluated".
-  CHECK(module->status() == kEvaluated || module->status() == kErrored);
+  // 1. Assert: module.[[AsyncEvaluating]] is true.
+  DCHECK(module->IsAsyncEvaluating());
 
-  // 2. If module.[[AsyncEvaluating]] is false,
-  if (!module->async_evaluating()) {
-    //  a. Assert: module.[[EvaluationError]] is not undefined.
-    CHECK_EQ(module->status(), kErrored);
-
-    //  b. Return undefined.
-    return;
-  }
-
-  // 3. Assert: module.[[EvaluationError]] is undefined.
+  // 2. Assert: module.[[EvaluationError]] is undefined.
   CHECK_EQ(module->status(), kEvaluated);
 
-  // 4. Set module.[[AsyncEvaluating]] to false.
-  module->set_async_evaluating(false);
+  // 3. Set module.[[AsyncEvaluating]] to false.
+  isolate->DidFinishModuleAsyncEvaluation(module->async_evaluating_ordinal());
+  module->set_async_evaluating_ordinal(kAsyncEvaluateDidFinish);
 
-  // 5. For each Module m of module.[[AsyncParentModules]], do
-  for (int i = 0; i < module->AsyncParentModuleCount(); i++) {
-    Handle<SourceTextModule> m = module->GetAsyncParentModule(isolate, i);
+  // 4. If module.[[TopLevelCapability]] is not empty, then
+  if (!module->top_level_capability().IsUndefined(isolate)) {
+    //  a. Assert: module.[[CycleRoot]] is equal to module.
+    DCHECK_EQ(*module->GetCycleRoot(isolate), *module);
 
-    //  a. Decrement m.[[PendingAsyncDependencies]] by 1.
-    m->DecrementPendingAsyncDependencies();
+    //   i. Perform ! Call(module.[[TopLevelCapability]].[[Resolve]], undefined,
+    //                     «undefined»).
+    Handle<JSPromise> capability(
+        JSPromise::cast(module->top_level_capability()), isolate);
+    JSPromise::Resolve(capability, isolate->factory()->undefined_value())
+        .ToHandleChecked();
+  }
 
-    //  b. If m.[[PendingAsyncDependencies]] is 0 and m.[[EvaluationError]] is
-    //     undefined, then
-    if (!m->HasPendingAsyncDependencies() && m->status() == kEvaluated) {
-      //   i. Assert: m.[[AsyncEvaluating]] is true.
-      DCHECK(m->async_evaluating());
+  // 5. Let execList be a new empty List.
+  Zone zone(isolate->allocator(), ZONE_NAME);
+  AsyncParentCompletionSet exec_list(&zone);
 
-      // ii. If m.[[CycleRoot]].[[EvaluationError]] is not undefined,
-      //      return undefined.
-      if (m->GetCycleRoot(isolate)->status() == kErrored) {
-        return;
-      }
+  // 6. Perform ! GatherAsyncParentCompletions(module, execList).
+  GatherAsyncParentCompletions(isolate, &zone, module, &exec_list);
+
+  // 7. Let sortedExecList be a List of elements that are the elements of
+  //    execList, in the order in which they had their [[AsyncEvaluating]]
+  //    fields set to true in InnerModuleEvaluation.
+  //
+  // This step is implemented by AsyncParentCompletionSet, which is a set
+  // ordered on async_evaluating_ordinal.
 
-      //  iii. If m.[[Async]] is true, then
-      if (m->async()) {
-        //    1. Perform ! ExecuteAsyncModule(m).
-        ExecuteAsyncModule(isolate, m);
+  // 8. Assert: All elements of sortedExecList have their [[AsyncEvaluating]]
+  //    field set to true, [[PendingAsyncDependencies]] field set to 0 and
+  //    [[EvaluationError]] field set to undefined.
+#ifdef DEBUG
+  for (Handle<SourceTextModule> m : exec_list) {
+    DCHECK(m->IsAsyncEvaluating());
+    DCHECK(!m->HasPendingAsyncDependencies());
+    DCHECK_NE(m->status(), kErrored);
+  }
+#endif
+
+  // 9. For each Module m of sortedExecList, do
+  for (Handle<SourceTextModule> m : exec_list) {
+    //  i. If m.[[AsyncEvaluating]] is false, then
+    if (!m->IsAsyncEvaluating()) {
+      //   a. Assert: m.[[EvaluatingError]] is not empty.
+      DCHECK_EQ(m->status(), kErrored);
+    } else if (m->async()) {
+      //  ii. Otherwise, if m.[[Async]] is *true*, then
+      //   a. Perform ! ExecuteAsyncModule(m).
+      ExecuteAsyncModule(isolate, m);
+    } else {
+      //  iii. Otherwise,
+      //   a. Let _result_ be m.ExecuteModule().
+      Handle<Object> unused_result;
+      //   b. If _result_ is an abrupt completion,
+      if (!ExecuteModule(isolate, m).ToHandle(&unused_result)) {
+        //    1. Perform ! AsyncModuleExecutionRejected(m, result.[[Value]]).
+        Handle<Object> exception(isolate->pending_exception(), isolate);
+        isolate->clear_pending_exception();
+        AsyncModuleExecutionRejected(isolate, m, exception);
       } else {
-        // iv. Otherwise,
-        //    1. Let result be m.ExecuteModule().
-        //    2. If result is a normal completion,
-        Handle<Object> unused_result;
-        if (ExecuteModule(isolate, m).ToHandle(&unused_result)) {
-          //     a. Perform ! AsyncModuleExecutionFulfilled(m).
-          AsyncModuleExecutionFulfilled(isolate, m);
-        } else {
-          //  3. Otherwise,
-          //     a. Perform ! AsyncModuleExecutionRejected(m,
-          //                                               result.[[Value]]).
-          Handle<Object> exception(isolate->pending_exception(), isolate);
-          isolate->clear_pending_exception();
-          AsyncModuleExecutionRejected(isolate, m, exception);
+        //   c. Otherwise,
+        //    1. Set m.[[AsyncEvaluating]] to false.
+        isolate->DidFinishModuleAsyncEvaluation(m->async_evaluating_ordinal());
+        m->set_async_evaluating_ordinal(kAsyncEvaluateDidFinish);
+
+        //    2. If m.[[TopLevelCapability]] is not empty, then
+        if (!m->top_level_capability().IsUndefined(isolate)) {
+          //  i. Assert: m.[[CycleRoot]] is equal to m.
+          DCHECK_EQ(*m->GetCycleRoot(isolate), *m);
+
+          //  ii. Perform ! Call(m.[[TopLevelCapability]].[[Resolve]],
+          //                     undefined, «undefined»).
+          Handle<JSPromise> capability(
+              JSPromise::cast(m->top_level_capability()), isolate);
+          JSPromise::Resolve(capability, isolate->factory()->undefined_value())
+              .ToHandleChecked();
         }
       }
     }
   }
 
-  // 6. If module.[[TopLevelCapability]] is not undefined, then
-  if (!module->top_level_capability().IsUndefined(isolate)) {
-    //  a. Assert: module.[[DFSIndex]] is equal to module.[[DFSAncestorIndex]].
-    DCHECK_EQ(module->dfs_index(), module->dfs_ancestor_index());
-
-    //  b. Perform ! Call(module.[[TopLevelCapability]].[[Resolve]],
-    //                    undefined, «undefined»).
-    Handle<JSPromise> capability(
-        JSPromise::cast(module->top_level_capability()), isolate);
-    JSPromise::Resolve(capability, isolate->factory()->undefined_value())
-        .ToHandleChecked();
-  }
-
-  // 7. Return undefined.
+  // 10. Return undefined.
 }
 
 void SourceTextModule::AsyncModuleExecutionRejected(
@@ -804,7 +881,7 @@ void SourceTextModule::AsyncModuleExecutionRejected(
   CHECK(module->status() == kEvaluated || module->status() == kErrored);
 
   // 2. If module.[[AsyncEvaluating]] is false,
-  if (!module->async_evaluating()) {
+  if (!module->IsAsyncEvaluating()) {
     //  a. Assert: module.[[EvaluationError]] is not undefined.
     CHECK_EQ(module->status(), kErrored);
 
@@ -816,7 +893,8 @@ void SourceTextModule::AsyncModuleExecutionRejected(
   module->RecordError(isolate, exception);
 
   // 5. Set module.[[AsyncEvaluating]] to false.
-  module->set_async_evaluating(false);
+  isolate->DidFinishModuleAsyncEvaluation(module->async_evaluating_ordinal());
+  module->set_async_evaluating_ordinal(kAsyncEvaluateDidFinish);
 
   // 6. For each Module m of module.[[AsyncParentModules]], do
   for (int i = 0; i < module->AsyncParentModuleCount(); i++) {
@@ -835,8 +913,8 @@ void SourceTextModule::AsyncModuleExecutionRejected(
 
   // 7. If module.[[TopLevelCapability]] is not undefined, then
   if (!module->top_level_capability().IsUndefined(isolate)) {
-    //  a. Assert: module.[[DFSIndex]] is equal to module.[[DFSAncestorIndex]].
-    DCHECK(module->dfs_index() == module->dfs_ancestor_index());
+    //  a. Assert: module.[[CycleRoot]] is equal to module.
+    DCHECK_EQ(*module->GetCycleRoot(isolate), *module);
 
     //  b. Perform ! Call(module.[[TopLevelCapability]].[[Reject]],
     //                    undefined, «error»).
@@ -857,7 +935,8 @@ void SourceTextModule::ExecuteAsyncModule(Isolate* isolate,
   DCHECK(module->async());
 
   // 3. Set module.[[AsyncEvaluating]] to true.
-  module->set_async_evaluating(true);
+  module->set_async_evaluating_ordinal(
+      isolate->NextModuleAsyncEvaluatingOrdinal());
 
   // 4. Let capability be ! NewPromiseCapability(%Promise%).
   Handle<JSPromise> capability = isolate->factory()->NewJSPromise();
@@ -1059,7 +1138,7 @@ MaybeHandle<Object> SourceTextModule::InnerModuleEvaluation(
         }
       }
       //     v. If requiredModule.[[AsyncEvaluating]] is true, then
-      if (required_module->async_evaluating()) {
+      if (required_module->IsAsyncEvaluating()) {
         //      1. Set module.[[PendingAsyncDependencies]] to
         //         module.[[PendingAsyncDependencies]] + 1.
         module->IncrementPendingAsyncDependencies();
@@ -1081,16 +1160,26 @@ MaybeHandle<Object> SourceTextModule::InnerModuleEvaluation(
   // synchronous modules, but return undefined for AsyncModules.
   Handle<Object> result = isolate->factory()->undefined_value();
 
-  // 14. If module.[[PendingAsyncDependencies]] is > 0, set
-  //     module.[[AsyncEvaluating]] to true.
-  if (module->HasPendingAsyncDependencies()) {
-    module->set_async_evaluating(true);
-  } else if (module->async()) {
-    // 15. Otherwise, if module.[[Async]] is true,
-    //     perform ! ExecuteAsyncModule(module).
-    SourceTextModule::ExecuteAsyncModule(isolate, module);
+  // 14. If module.[[PendingAsyncDependencies]] > 0 or module.[[Async]] is
+  //     true, then
+  if (module->HasPendingAsyncDependencies() || module->async()) {
+    // a. Assert: module.[[AsyncEvaluating]] is false and was never previously
+    //     set to true.
+    DCHECK_EQ(module->async_evaluating_ordinal(), kNotAsyncEvaluated);
+
+    // b. Set module.[[AsyncEvaluating]] to true.
+    // NOTE: The order in which modules transition to async evaluating is
+    // significant.
+    module->set_async_evaluating_ordinal(
+        isolate->NextModuleAsyncEvaluatingOrdinal());
+
+    // c. If module.[[PendingAsyncDependencies]] is 0,
+    //    perform ! ExecuteAsyncModule(_module_).
+    if (!module->HasPendingAsyncDependencies()) {
+      SourceTextModule::ExecuteAsyncModule(isolate, module);
+    }
   } else {
-    // 16. Otherwise, perform ? module.ExecuteModule().
+    // 15. Otherwise, perform ? module.ExecuteModule().
     ASSIGN_RETURN_ON_EXCEPTION(isolate, result, ExecuteModule(isolate, module),
                                Object);
   }
diff --git a/deps/v8/src/objects/source-text-module.h b/deps/v8/src/objects/source-text-module.h
index f2960d80ea1904..b91d1e5080e776 100644
--- a/deps/v8/src/objects/source-text-module.h
+++ b/deps/v8/src/objects/source-text-module.h
@@ -7,6 +7,7 @@
 
 #include "src/objects/module.h"
 #include "src/objects/promise.h"
+#include "src/zone/zone-containers.h"
 #include "torque-generated/bit-fields-tq.h"
 
 // Has to be the last include (doesn't have include guards):
@@ -69,10 +70,16 @@ class SourceTextModule
       SubclassBodyDescriptor<Module::BodyDescriptor,
                              FixedBodyDescriptor<kCodeOffset, kSize, kSize>>;
 
+  static constexpr unsigned kFirstAsyncEvaluatingOrdinal = 2;
+
  private:
   friend class Factory;
   friend class Module;
 
+  struct AsyncEvaluatingOrdinalCompare;
+  using AsyncParentCompletionSet =
+      ZoneSet<Handle<SourceTextModule>, AsyncEvaluatingOrdinalCompare>;
+
   // Appends a tuple of module and generator to the async parent modules
   // ArrayList.
   inline static void AddAsyncParentModule(Isolate* isolate,
@@ -90,6 +97,8 @@ class SourceTextModule
   // Returns the number of async parent modules for a given async child.
   inline int AsyncParentModuleCount();
 
+  inline bool IsAsyncEvaluating() const;
+
   inline bool HasPendingAsyncDependencies();
   inline void IncrementPendingAsyncDependencies();
   inline void DecrementPendingAsyncDependencies();
@@ -97,13 +106,26 @@ class SourceTextModule
   // Bits for flags.
   DEFINE_TORQUE_GENERATED_SOURCE_TEXT_MODULE_FLAGS()
 
-  // async_evaluating, top_level_capability, pending_async_dependencies, and
-  // async_parent_modules are used exclusively during evaluation of async
+  // async_evaluating_ordinal, top_level_capability, pending_async_dependencies,
+  // and async_parent_modules are used exclusively during evaluation of async
   // modules and the modules which depend on them.
   //
-  // Whether or not this module is async and evaluating or currently evaluating
-  // an async child.
-  DECL_BOOLEAN_ACCESSORS(async_evaluating)
+  // If >1, this module is async and evaluating or currently evaluating an async
+  // child. The integer is an ordinal for when this module first started async
+  // evaluation and is used for sorting async parent modules when determining
+  // which parent module can start executing after an async evaluation
+  // completes.
+  //
+  // If 1, this module has finished async evaluating.
+  //
+  // If 0, this module is not async or has not been async evaluated.
+  static constexpr unsigned kNotAsyncEvaluated = 0;
+  static constexpr unsigned kAsyncEvaluateDidFinish = 1;
+  STATIC_ASSERT(kNotAsyncEvaluated < kAsyncEvaluateDidFinish);
+  STATIC_ASSERT(kAsyncEvaluateDidFinish < kFirstAsyncEvaluatingOrdinal);
+  STATIC_ASSERT(kMaxModuleAsyncEvaluatingOrdinal ==
+                AsyncEvaluatingOrdinalBits::kMax);
+  DECL_PRIMITIVE_ACCESSORS(async_evaluating_ordinal, unsigned)
 
   // The top level promise capability of this module. Will only be defined
   // for cycle roots.
@@ -149,6 +171,10 @@ class SourceTextModule
                                Handle<SourceTextModule> module, Zone* zone,
                                UnorderedModuleSet* visited);
 
+  static void GatherAsyncParentCompletions(Isolate* isolate, Zone* zone,
+                                           Handle<SourceTextModule> start,
+                                           AsyncParentCompletionSet* exec_list);
+
   // Implementation of spec concrete method Evaluate.
   static V8_WARN_UNUSED_RESULT MaybeHandle<Object> EvaluateMaybeAsync(
       Isolate* isolate, Handle<SourceTextModule> module);
diff --git a/deps/v8/src/objects/source-text-module.tq b/deps/v8/src/objects/source-text-module.tq
index a9e3ee3db9a793..f2eb8e2ce6fe3d 100644
--- a/deps/v8/src/objects/source-text-module.tq
+++ b/deps/v8/src/objects/source-text-module.tq
@@ -6,7 +6,7 @@ type SourceTextModuleInfo extends FixedArray;
 
 bitfield struct SourceTextModuleFlags extends uint31 {
   async: bool: 1 bit;
-  async_evaluating: bool: 1 bit;
+  async_evaluating_ordinal: uint32: 30 bit;
 }
 
 @generateCppClass
diff --git a/deps/v8/test/mjsunit/harmony/modules-import-rqstd-order-async-subgraph.mjs b/deps/v8/test/mjsunit/harmony/modules-import-rqstd-order-async-subgraph.mjs
new file mode 100644
index 00000000000000..317349b06300db
--- /dev/null
+++ b/deps/v8/test/mjsunit/harmony/modules-import-rqstd-order-async-subgraph.mjs
@@ -0,0 +1,11 @@
+// Copyright 2021 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-top-level-await
+
+import "modules-skip-async-subgraph-start.mjs"
+
+assertEquals(globalThis.test_order, [
+  'async before', 'async after', '1', '2', 'x', 'start'
+]);
diff --git a/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-1.mjs b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-1.mjs
new file mode 100644
index 00000000000000..d4bc01d8419489
--- /dev/null
+++ b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-1.mjs
@@ -0,0 +1,12 @@
+// Copyright 2021 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-top-level-await
+
+import "modules-skip-async-subgraph-async.mjs"
+
+if (globalThis.test_order === undefined) {
+  globalThis.test_order = [];
+}
+globalThis.test_order.push('1');
diff --git a/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-2.mjs b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-2.mjs
new file mode 100644
index 00000000000000..ee37caffd4a99f
--- /dev/null
+++ b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-2.mjs
@@ -0,0 +1,12 @@
+// Copyright 2021 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-top-level-await
+
+import "modules-skip-async-subgraph-async.mjs"
+
+if (globalThis.test_order === undefined) {
+  globalThis.test_order = [];
+}
+globalThis.test_order.push('2');
diff --git a/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-async.mjs b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-async.mjs
new file mode 100644
index 00000000000000..447f801a8ad8de
--- /dev/null
+++ b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-async.mjs
@@ -0,0 +1,12 @@
+// Copyright 2021 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-top-level-await
+
+if (globalThis.test_order === undefined) {
+  globalThis.test_order = [];
+}
+globalThis.test_order.push('async before');
+await 0;
+globalThis.test_order.push('async after');
diff --git a/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-start.mjs b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-start.mjs
new file mode 100644
index 00000000000000..861907a9dd7ff4
--- /dev/null
+++ b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-start.mjs
@@ -0,0 +1,14 @@
+// Copyright 2021 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-top-level-await
+
+import "modules-skip-async-subgraph-1.mjs"
+import "modules-skip-async-subgraph-2.mjs"
+import "modules-skip-async-subgraph-x.mjs"
+
+if (globalThis.test_order === undefined) {
+  globalThis.test_order = [];
+}
+globalThis.test_order.push('start');
diff --git a/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-x.mjs b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-x.mjs
new file mode 100644
index 00000000000000..813a9bb870e78b
--- /dev/null
+++ b/deps/v8/test/mjsunit/harmony/modules-skip-async-subgraph-x.mjs
@@ -0,0 +1,12 @@
+// Copyright 2021 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-top-level-await
+
+import "modules-skip-async-subgraph-1.mjs"
+
+if (globalThis.test_order === undefined) {
+  globalThis.test_order = [];
+}
+globalThis.test_order.push('x');