diff --git a/lib/internal/http2/compat.js b/lib/internal/http2/compat.js
index 173fa3429bec52..06d283a4b8bbea 100644
--- a/lib/internal/http2/compat.js
+++ b/lib/internal/http2/compat.js
@@ -229,6 +229,13 @@ function onStreamCloseRequest() {
   req.emit('close');
 }
 
+function onStreamTimeout(kind) {
+  return function onStreamTimeout() {
+    const obj = this[kind];
+    obj.emit('timeout');
+  };
+}
+
 class Http2ServerRequest extends Readable {
   constructor(stream, headers, options, rawHeaders) {
     super(options);
@@ -251,6 +258,7 @@ class Http2ServerRequest extends Readable {
     stream.on('error', onStreamError);
     stream.on('aborted', onStreamAbortedRequest);
     stream.on('close', onStreamCloseRequest);
+    stream.on('timeout', onStreamTimeout(kRequest));
     this.on('pause', onRequestPause);
     this.on('resume', onRequestResume);
   }
@@ -403,6 +411,7 @@ class Http2ServerResponse extends Stream {
     stream.on('aborted', onStreamAbortedResponse);
     stream.on('close', onStreamCloseResponse);
     stream.on('wantTrailers', onStreamTrailersReady);
+    stream.on('timeout', onStreamTimeout(kResponse));
   }
 
   // User land modules such as finalhandler just check truthiness of this
diff --git a/test/parallel/test-http2-compat-serverrequest-settimeout.js b/test/parallel/test-http2-compat-serverrequest-settimeout.js
index f7189161802301..e7cad0975621dd 100644
--- a/test/parallel/test-http2-compat-serverrequest-settimeout.js
+++ b/test/parallel/test-http2-compat-serverrequest-settimeout.js
@@ -13,6 +13,11 @@ server.on('request', (req, res) => {
   req.setTimeout(msecs, common.mustCall(() => {
     res.end();
   }));
+  // Note: The timeout is reset in the call to res.end() above. The 'timeout'
+  // event listener might be called more than once if it takes more than 1ms
+  // to close, so use the `once` event listener here. (This is more likely to
+  // happen in Node 8 than 10.)
+  res.once('timeout', common.mustCall());
   res.on('finish', common.mustCall(() => {
     req.setTimeout(msecs, common.mustNotCall());
     process.nextTick(() => {
diff --git a/test/parallel/test-http2-compat-serverresponse-settimeout.js b/test/parallel/test-http2-compat-serverresponse-settimeout.js
index bb09633727ccf7..22a9659633c0b1 100644
--- a/test/parallel/test-http2-compat-serverresponse-settimeout.js
+++ b/test/parallel/test-http2-compat-serverresponse-settimeout.js
@@ -13,6 +13,11 @@ server.on('request', (req, res) => {
   res.setTimeout(msecs, common.mustCall(() => {
     res.end();
   }));
+  // Note: The timeout is reset in the call to res.end() above. The 'timeout'
+  // event listener might be called more than once if it takes more than 1ms
+  // to close, so use the `once` event listener here. (This is more likely to
+  // happen in Node 8 than 10.)
+  res.once('timeout', common.mustCall());
   res.on('finish', common.mustCall(() => {
     res.setTimeout(msecs, common.mustNotCall());
     process.nextTick(() => {