diff --git a/test/parallel/test-http2-server-destroy-before-priority.js b/test/parallel/test-http2-server-destroy-before-priority.js
new file mode 100644
index 00000000000000..74d7c011ba0be1
--- /dev/null
+++ b/test/parallel/test-http2-server-destroy-before-priority.js
@@ -0,0 +1,41 @@
+// Flags: --expose-http2
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const assert = require('assert');
+const http2 = require('http2');
+
+const server = http2.createServer();
+
+// Test that ERR_HTTP2_INVALID_STREAM is thrown when a stream is destroyed
+// before calling stream.priority
+server.on('stream', common.mustCall(onStream));
+
+function onStream(stream, headers, flags) {
+  stream.session.destroy();
+  assert.throws(() => stream.priority(),
+                common.expectsError({
+                  code: 'ERR_HTTP2_INVALID_STREAM',
+                  message: /^The stream has been destroyed$/
+                }));
+}
+
+server.listen(0);
+
+server.on('listening', common.mustCall(() => {
+
+  const client = http2.connect(`http://localhost:${server.address().port}`);
+
+  const req = client.request({ ':path': '/' });
+
+  req.on('response', common.mustNotCall());
+  req.resume();
+  req.on('end', common.mustCall(() => {
+    server.close();
+    client.destroy();
+  }));
+  req.end();
+
+}));
diff --git a/test/parallel/test-http2-server-destroy-before-rst.js b/test/parallel/test-http2-server-destroy-before-rst.js
new file mode 100644
index 00000000000000..f066e76b5f97de
--- /dev/null
+++ b/test/parallel/test-http2-server-destroy-before-rst.js
@@ -0,0 +1,41 @@
+// Flags: --expose-http2
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const assert = require('assert');
+const http2 = require('http2');
+
+const server = http2.createServer();
+
+// Test that ERR_HTTP2_INVALID_STREAM is thrown when a stream is destroyed
+// before calling stream.rstStream
+server.on('stream', common.mustCall(onStream));
+
+function onStream(stream, headers, flags) {
+  stream.session.destroy();
+  assert.throws(() => stream.rstStream(),
+                common.expectsError({
+                  code: 'ERR_HTTP2_INVALID_STREAM',
+                  message: /^The stream has been destroyed$/
+                }));
+}
+
+server.listen(0);
+
+server.on('listening', common.mustCall(() => {
+
+  const client = http2.connect(`http://localhost:${server.address().port}`);
+
+  const req = client.request({ ':path': '/' });
+
+  req.on('response', common.mustNotCall());
+  req.resume();
+  req.on('end', common.mustCall(() => {
+    server.close();
+    client.destroy();
+  }));
+  req.end();
+
+}));
diff --git a/test/parallel/test-http2-server-destroy-before-state.js b/test/parallel/test-http2-server-destroy-before-state.js
new file mode 100644
index 00000000000000..f5dce3e30a272d
--- /dev/null
+++ b/test/parallel/test-http2-server-destroy-before-state.js
@@ -0,0 +1,37 @@
+// Flags: --expose-http2
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const assert = require('assert');
+const http2 = require('http2');
+
+const server = http2.createServer();
+
+// Test that stream.state getter returns and empty object
+// if the stream session has been destroyed
+server.on('stream', common.mustCall(onStream));
+
+function onStream(stream, headers, flags) {
+  stream.session.destroy();
+  assert.deepStrictEqual(Object.create(null), stream.state);
+}
+
+server.listen(0);
+
+server.on('listening', common.mustCall(() => {
+
+  const client = http2.connect(`http://localhost:${server.address().port}`);
+
+  const req = client.request({ ':path': '/' });
+
+  req.on('response', common.mustNotCall());
+  req.resume();
+  req.on('end', common.mustCall(() => {
+    server.close();
+    client.destroy();
+  }));
+  req.end();
+
+}));