diff --git a/doc/api/assert.md b/doc/api/assert.md
index 70e13f3b87760c..14de5af2ed9561 100644
--- a/doc/api/assert.md
+++ b/doc/api/assert.md
@@ -125,12 +125,13 @@ changes:
 * `expected` {any}
 * `message` {any}
 
-Generally identical to `assert.deepEqual()` with two exceptions:
+Generally identical to `assert.deepEqual()` with three exceptions:
 
 1. Primitive values are compared using the [Strict Equality Comparison][]
   ( `===` ).
 2. [`[[Prototype]]`][prototype-spec] of objects are compared using
   the [Strict Equality Comparison][] too.
+3. [Type tags][Object.prototype.toString()] of objects should be the same.
 
 ```js
 const assert = require('assert');
@@ -141,6 +142,25 @@ assert.deepEqual({a: 1}, {a: '1'});
 assert.deepStrictEqual({a: 1}, {a: '1'});
 // AssertionError: { a: 1 } deepStrictEqual { a: '1' }
 // because 1 !== '1' using strict equality
+
+// The following objects don't have own properties
+const date = new Date();
+const object = {};
+const fakeDate = {};
+
+Object.setPrototypeOf(fakeDate, Date.prototype);
+
+assert.deepEqual(object, fakeDate);
+// OK, doesn't check [[Prototype]]
+assert.deepStrictEqual(object, fakeDate);
+// AssertionError: {} deepStrictEqual Date {}
+// Different [[Prototype]]
+
+assert.deepEqual(date, fakeDate);
+// OK, doesn't check type tags
+assert.deepStrictEqual(date, fakeDate);
+// AssertionError: 2017-03-11T14:25:31.849Z deepStrictEqual Date {}
+// Different type tags
 ```
 
 If the values are not equal, an `AssertionError` is thrown with a `message`
@@ -579,4 +599,5 @@ For more information, see
 [SameValueZero]: https://tc39.github.io/ecma262/#sec-samevaluezero
 [prototype-spec]: https://tc39.github.io/ecma262/#sec-ordinary-object-internal-methods-and-internal-slots
 [mdn-equality-guide]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Equality_comparisons_and_sameness
-[enumerable "own" properties]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Enumerability_and_ownership_of_properties
\ No newline at end of file
+[enumerable "own" properties]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Enumerability_and_ownership_of_properties
+[Object.prototype.toString()]: https://tc39.github.io/ecma262/#sec-object.prototype.tostring
diff --git a/lib/assert.js b/lib/assert.js
index 3183784dbfc42d..df575c0f169b22 100644
--- a/lib/assert.js
+++ b/lib/assert.js
@@ -200,6 +200,10 @@ function _deepEqual(actual, expected, strict, memos) {
     if (Object.getPrototypeOf(actual) !== Object.getPrototypeOf(expected)) {
       return false;
     }
+
+    if (actualTag !== expectedTag) {
+      return false;
+    }
   }
 
   // Do fast checks for builtin types.
diff --git a/test/parallel/test-assert-checktag.js b/test/parallel/test-assert-checktag.js
new file mode 100644
index 00000000000000..ae409c7250350e
--- /dev/null
+++ b/test/parallel/test-assert-checktag.js
@@ -0,0 +1,61 @@
+'use strict';
+require('../common');
+const assert = require('assert');
+const util = require('util');
+
+// Template tag function turning an error message into a RegExp
+// for assert.throws()
+function re(literals, ...values) {
+  let result = literals[0];
+  for (const [i, value] of values.entries()) {
+    const str = util.inspect(value);
+    // Need to escape special characters.
+    result += str.replace(/[\\^$.*+?()[\]{}|=!<>:-]/g, '\\$&');
+    result += literals[i + 1];
+  }
+  return new RegExp('^AssertionError: ' + result + '$');
+}
+
+// Turn off no-restricted-properties because we are testing deepEqual!
+/* eslint-disable no-restricted-properties */
+
+// See https://github.com/nodejs/node/issues/10258
+{
+  const date = new Date('2016');
+  function FakeDate() {}
+  FakeDate.prototype = Date.prototype;
+  const fake = new FakeDate();
+
+  assert.doesNotThrow(() => assert.deepEqual(date, fake));
+  assert.doesNotThrow(() => assert.deepEqual(fake, date));
+
+  // For deepStrictEqual we check the runtime type,
+  // then reveal the fakeness of the fake date
+  assert.throws(() => assert.deepStrictEqual(date, fake),
+                re`${date} deepStrictEqual Date {}`);
+  assert.throws(() => assert.deepStrictEqual(fake, date),
+                re`Date {} deepStrictEqual ${date}`);
+}
+
+{  // At the moment global has its own type tag
+  const fakeGlobal = {};
+  Object.setPrototypeOf(fakeGlobal, Object.getPrototypeOf(global));
+  for (const prop of Object.keys(global)) {
+    fakeGlobal[prop] = global[prop];
+  }
+  assert.doesNotThrow(() => assert.deepEqual(fakeGlobal, global));
+  // Message will be truncated anyway, don't validate
+  assert.throws(() => assert.deepStrictEqual(fakeGlobal, global));
+}
+
+{ // At the moment process has its own type tag
+  const fakeProcess = {};
+  Object.setPrototypeOf(fakeProcess, Object.getPrototypeOf(process));
+  for (const prop of Object.keys(process)) {
+    fakeProcess[prop] = process[prop];
+  }
+  assert.doesNotThrow(() => assert.deepEqual(fakeProcess, process));
+  // Message will be truncated anyway, don't validate
+  assert.throws(() => assert.deepStrictEqual(fakeProcess, process));
+}
+/* eslint-enable */