diff --git a/spec-dtslint/operators/window-spec.ts b/spec-dtslint/operators/window-spec.ts
index 683e6a85e6..1f65abeb1e 100644
--- a/spec-dtslint/operators/window-spec.ts
+++ b/spec-dtslint/operators/window-spec.ts
@@ -6,5 +6,10 @@ it('should infer correctly', () => {
 });
 
 it('should enforce types', () => {
-  of(1).pipe(window('')); // $ExpectError
+  of(1).pipe(window()); // $ExpectError
+  of(1).pipe(window(6)); // $ExpectError
+});
+
+it('should support Promises', () => {
+  of(1, 2, 3).pipe(window(Promise.resolve('foo'))); // $ExpectType Observable<Observable<number>>
 });
diff --git a/spec/operators/window-spec.ts b/spec/operators/window-spec.ts
index 5eb2d9aff9..929977e04c 100644
--- a/spec/operators/window-spec.ts
+++ b/spec/operators/window-spec.ts
@@ -1,7 +1,8 @@
-import { window, mergeMap } from 'rxjs/operators';
+import { window, mergeMap, take } from 'rxjs/operators';
 import { TestScheduler } from 'rxjs/testing';
-import { EMPTY, of, Observable } from 'rxjs';
+import { EMPTY, of, Observable, interval } from 'rxjs';
 import { observableMatcher } from '../helpers/observableMatcher';
+import { expect } from 'chai';
 
 /** @test {window} */
 describe('window', () => {
@@ -280,4 +281,43 @@ describe('window', () => {
       expectSubscriptions(closings.subscriptions).toBe(closingSubs);
     });
   });
+
+  it('should window when Promise resolves', (done) => {
+    const e1 = interval(3).pipe(take(5));
+    let pos = 0;
+    const result: number[][] = [[], []];
+    const expected = [
+      [0, 1],
+      [2, 3, 4],
+    ];
+
+    e1.pipe(window(new Promise<void>((resolve) => setTimeout(() => resolve(), 8)))).subscribe({
+      next: (x) => {
+        x.subscribe({
+          next: (v) => result[pos].push(v),
+          complete: () => pos++,
+        });
+      },
+      error: () => done(new Error('should not be called')),
+      complete: () => {
+        expect(result).to.deep.equal(expected);
+        done();
+      },
+    });
+  });
+
+  it('should raise error when Promise rejects', (done) => {
+    const e1 = interval(1).pipe(take(5));
+    const error = new Error('err');
+
+    e1.pipe(window(Promise.reject(error))).subscribe({
+      error: (err) => {
+        expect(err).to.be.an('error');
+        done();
+      },
+      complete: () => {
+        done(new Error('should not be called'));
+      },
+    });
+  });
 });
diff --git a/src/internal/operators/window.ts b/src/internal/operators/window.ts
index 31ef626f60..b8250cbc2e 100644
--- a/src/internal/operators/window.ts
+++ b/src/internal/operators/window.ts
@@ -1,9 +1,10 @@
 import { Observable } from '../Observable';
-import { OperatorFunction } from '../types';
+import { OperatorFunction, ObservableInput } from '../types';
 import { Subject } from '../Subject';
 import { operate } from '../util/lift';
 import { createOperatorSubscriber } from './OperatorSubscriber';
 import { noop } from '../util/noop';
+import { innerFrom } from '../observable/innerFrom';
 
 /**
  * Branch out the source Observable values as a nested Observable whenever
@@ -17,8 +18,9 @@ import { noop } from '../util/noop';
  * Returns an Observable that emits windows of items it collects from the source
  * Observable. The output Observable emits connected, non-overlapping
  * windows. It emits the current window and opens a new one whenever the
- * Observable `windowBoundaries` emits an item. Because each window is an
- * Observable, the output is a higher-order Observable.
+ * `windowBoundaries` emits an item. `windowBoundaries` can be any type that
+ * `ObservableInput` accepts. It internally gets converted to an Observable.
+ * Because each window is an Observable, the output is a higher-order Observable.
  *
  * ## Example
  *
@@ -43,12 +45,12 @@ import { noop } from '../util/noop';
  * @see {@link windowWhen}
  * @see {@link buffer}
  *
- * @param {Observable<any>} windowBoundaries An Observable that completes the
+ * @param windowBoundaries An `ObservableInput` that completes the
  * previous window and starts a new window.
  * @return A function that returns an Observable of windows, which are
  * Observables emitting values of the source Observable.
  */
-export function window<T>(windowBoundaries: Observable<any>): OperatorFunction<T, Observable<T>> {
+export function window<T>(windowBoundaries: ObservableInput<any>): OperatorFunction<T, Observable<T>> {
   return operate((source, subscriber) => {
     let windowSubject: Subject<T> = new Subject<T>();
 
@@ -73,7 +75,7 @@ export function window<T>(windowBoundaries: Observable<any>): OperatorFunction<T
     );
 
     // Subscribe to the window boundaries.
-    windowBoundaries.subscribe(
+    innerFrom(windowBoundaries).subscribe(
       createOperatorSubscriber(
         subscriber,
         () => {