diff --git a/lib/internal/http2/compat.js b/lib/internal/http2/compat.js
index 88879484ebaab7..14f20bc3d4583d 100644
--- a/lib/internal/http2/compat.js
+++ b/lib/internal/http2/compat.js
@@ -705,12 +705,15 @@ class Http2ServerResponse extends Stream {
   }
 }
 
-function onServerStream(ServerRequest, ServerResponse,
+function onServerStream(ServerRequest, ServerResponse, kStreamEventsComposite,
                         stream, headers, flags, rawHeaders) {
   const server = this;
   const request = new ServerRequest(stream, headers, undefined, rawHeaders);
   const response = new ServerResponse(stream);
 
+  stream[kStreamEventsComposite].push(request);
+  stream[kStreamEventsComposite].push(response);
+
   // Check for the CONNECT method
   const method = headers[HTTP2_HEADER_METHOD];
   if (method === 'CONNECT') {
diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 39d456fb75905f..47e2408908b3f5 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -147,6 +147,7 @@ const kState = Symbol('state');
 const kType = Symbol('type');
 const kUpdateTimer = Symbol('update-timer');
 const kWriteGeneric = Symbol('write-generic');
+const kStreamEventsComposite = Symbol('streamEventsComposite');
 
 const kDefaultSocketTimeout = 2 * 60 * 1000;
 
@@ -1551,6 +1552,8 @@ class Http2Stream extends Duplex {
       trailersReady: false
     };
 
+    this[kStreamEventsComposite] = [];
+
     this.on('pause', streamOnPause);
   }
 
@@ -1640,7 +1643,17 @@ class Http2Stream extends Duplex {
       }
     }
 
-    this.emit('timeout');
+    // if there is no timeout event listener, destroy session
+    let hasTimeoutCallback = this.emit('timeout');
+    for (const component of this[kStreamEventsComposite]) {
+      if (component.emit('timeout')) {
+        hasTimeoutCallback = true;
+      }
+    }
+
+    if (!hasTimeoutCallback) {
+      this.session.destroy();
+    }
   }
 
   // true if the HEADERS frame has been sent
@@ -2662,7 +2675,8 @@ function setupCompat(ev) {
     this.on('stream', onServerStream.bind(
       this,
       this[kOptions].Http2ServerRequest,
-      this[kOptions].Http2ServerResponse)
+      this[kOptions].Http2ServerResponse,
+      kStreamEventsComposite)
     );
   }
 }
diff --git a/test/parallel/test-http2-compat-serverrequest-settimeout.js b/test/parallel/test-http2-compat-serverrequest-settimeout.js
index 81184d70752563..769486f6222d43 100644
--- a/test/parallel/test-http2-compat-serverrequest-settimeout.js
+++ b/test/parallel/test-http2-compat-serverrequest-settimeout.js
@@ -12,6 +12,10 @@ server.on('request', (req, res) => {
   req.setTimeout(msecs, common.mustCall(() => {
     res.end();
   }));
+
+  res.on('timeout', common.mustCall());
+  req.on('timeout', common.mustCall());
+
   res.on('finish', common.mustCall(() => {
     req.setTimeout(msecs, common.mustNotCall());
     process.nextTick(() => {