diff --git a/lib/assert.js b/lib/assert.js
index db0a2283e63db9..d76ea86db42299 100644
--- a/lib/assert.js
+++ b/lib/assert.js
@@ -600,6 +600,11 @@ function checkIsPromise(obj) {
   // Accept native ES6 promises and promises that are implemented in a similar
   // way. Do not accept thenables that use a function as `obj` and that have no
   // `catch` handler.
+
+  // TODO: thenables are checked up until they have the correct methods,
+  // but according to documentation, the `then` method should receive
+  // the `fulfill` and `reject` arguments as well or it may be never resolved.
+
   return isPromise(obj) ||
     obj !== null && typeof obj === 'object' &&
     typeof obj.then === 'function' &&
diff --git a/test/parallel/test-assert-async.js b/test/parallel/test-assert-async.js
index d461e403300b34..140bd05d1a3c8f 100644
--- a/test/parallel/test-assert-async.js
+++ b/test/parallel/test-assert-async.js
@@ -2,12 +2,34 @@
 const common = require('../common');
 const assert = require('assert');
 
-// Test assert.rejects() and assert.doesNotReject() by checking their
-// expected output and by verifying that they do not work sync
-
 // Run all tests in parallel and check their outcome at the end.
 const promises = [];
 
+// Thenable object without `catch` method,
+// shouldn't be considered as a valid Thenable
+const invalidThenable = {
+  then: (fulfill, reject) => {
+    fulfill();
+  },
+};
+
+// Function that returns a Thenable function,
+// a function with `catch` and `then` methods attached,
+// shouldn't be considered as a valid Thenable.
+const invalidThenableFunc = () => {
+  function f() {}
+
+  f.then = (fulfill, reject) => {
+    fulfill();
+  };
+  f.catch = () => {};
+
+  return f;
+};
+
+// Test assert.rejects() and assert.doesNotReject() by checking their
+// expected output and by verifying that they do not work sync
+
 // Check `assert.rejects`.
 {
   const rejectingFn = async () => assert.fail();
@@ -16,9 +38,34 @@ const promises = [];
     name: 'AssertionError',
     message: 'Failed'
   };
-  // `assert.rejects` accepts a function or a promise as first argument.
+
+  // `assert.rejects` accepts a function or a promise
+  // or a thenable as first argument.
   promises.push(assert.rejects(rejectingFn, errObj));
   promises.push(assert.rejects(rejectingFn(), errObj));
+
+  const validRejectingThenable = {
+    then: (fulfill, reject) => {
+      reject({ code: 'FAIL' });
+    },
+    catch: () => {}
+  };
+  promises.push(assert.rejects(validRejectingThenable, { code: 'FAIL' }));
+
+  // `assert.rejects` should not accept thenables that
+  // use a function as `obj` and that have no `catch` handler.
+  promises.push(assert.rejects(
+    assert.rejects(invalidThenable, {}),
+    {
+      code: 'ERR_INVALID_ARG_TYPE'
+    })
+  );
+  promises.push(assert.rejects(
+    assert.rejects(invalidThenableFunc, {}),
+    {
+      code: 'ERR_INVALID_RETURN_VALUE'
+    })
+  );
 }
 
 {
@@ -69,7 +116,8 @@ promises.push(assert.rejects(
 
 // Check `assert.doesNotReject`.
 {
-  // `assert.doesNotReject` accepts a function or a promise as first argument.
+  // `assert.doesNotReject` accepts a function or a promise
+  // or a thenable as first argument.
   const promise = assert.doesNotReject(() => new Map(), common.mustNotCall());
   promises.push(assert.rejects(promise, {
     message: 'Expected instance of Promise to be returned ' +
@@ -79,6 +127,28 @@ promises.push(assert.rejects(
   }));
   promises.push(assert.doesNotReject(async () => {}));
   promises.push(assert.doesNotReject(Promise.resolve()));
+
+  // `assert.doesNotReject` should not accept thenables that
+  // use a function as `obj` and that have no `catch` handler.
+  const validFulfillingThenable = {
+    then: (fulfill, reject) => {
+      fulfill();
+    },
+    catch: () => {}
+  };
+  promises.push(assert.doesNotReject(validFulfillingThenable));
+  promises.push(assert.rejects(
+    assert.doesNotReject(invalidThenable),
+    {
+      code: 'ERR_INVALID_ARG_TYPE'
+    })
+  );
+  promises.push(assert.rejects(
+    assert.doesNotReject(invalidThenableFunc),
+    {
+      code: 'ERR_INVALID_RETURN_VALUE'
+    })
+  );
 }
 
 {