diff --git a/Lib/_abcoll.py b/Lib/_abcoll.py
index a60d91e..e9f06a5 100644
--- a/Lib/_abcoll.py
+++ b/Lib/_abcoll.py
@@ -376,8 +376,9 @@
         return ValuesView(self)
 
     def __eq__(self, other):
-        return isinstance(other, Mapping) and \
-               dict(self.items()) == dict(other.items())
+        if not isinstance(other, Mapping):
+            return NotImplemented
+        return dict(self.items()) == dict(other.items())
 
     def __ne__(self, other):
         return not (self == other)
diff --git a/Lib/test/test_collections.py b/Lib/test/test_collections.py
index ded8b70..33deb78 100644
--- a/Lib/test/test_collections.py
+++ b/Lib/test/test_collections.py
@@ -1,6 +1,6 @@
 """Unit tests for collections.py."""
 
-import unittest, doctest
+import unittest, doctest, operator
 import inspect
 from test import support
 from collections import namedtuple, Counter, OrderedDict
@@ -230,6 +230,37 @@
             self.assertRaises(TypeError, C, name)
 
 
+    def validate_comparison(self, instance):
+        ops = ['lt', 'gt', 'le', 'ge', 'ne', 'or', 'and', 'xor', 'sub']
+        operators = {}
+        for op in ops:
+            name = '__' + op + '__'
+            operators[name] = getattr(operator, name)
+
+        class Other:
+            def __init__(self):
+                self.right_side = False
+            def __eq__(self, other):
+                self.right_side = True
+                return True
+            __lt__ = __eq__
+            __gt__ = __eq__
+            __le__ = __eq__
+            __ge__ = __eq__
+            __ne__ = __eq__
+            __ror__ = __eq__
+            __rand__ = __eq__
+            __rxor__ = __eq__
+            __rsub__ = __eq__
+
+        for name, op in operators.items():
+            if not hasattr(instance, name):
+                continue
+            other = Other()
+            op(instance, other)
+            self.assertTrue(other.right_side,'Right side not called for %s.%s'
+                            % (type(instance), name))
+
 class TestOneTrickPonyABCs(ABCTestCase):
 
     def test_Hashable(self):
@@ -398,6 +429,14 @@
             self.assertTrue(isinstance(sample(), Set))
             self.assertTrue(issubclass(sample, Set))
         self.validate_abstract_methods(Set, '__contains__', '__iter__', '__len__')
+        class MySet(Set):
+            def __contains__(self, x):
+                return False
+            def __len__(self):
+                return 0
+            def __iter__(self):
+                return iter([])
+        self.validate_comparison(MySet())
 
     def test_hash_Set(self):
         class OneTwoThreeSet(Set):
@@ -461,6 +500,14 @@
             self.assertTrue(issubclass(sample, Mapping))
         self.validate_abstract_methods(Mapping, '__contains__', '__iter__', '__len__',
             '__getitem__')
+        class MyMapping(collections.Mapping):
+            def __len__(self):
+                return 0
+            def __getitem__(self, i):
+                raise IndexError
+            def __iter__(self):
+                return iter(())
+        self.validate_comparison(MyMapping())
 
     def test_MutableMapping(self):
         for sample in [dict]:
diff --git a/Misc/NEWS b/Misc/NEWS
index 2304606..27dd6a4 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -54,6 +54,9 @@
 Library
 -------
 
+- Issue #8729: Return NotImplemented from collections.Mapping.__eq__ when
+  comparing to a non-mapping.
+
 - Issue #8774: tabnanny uses the encoding cookie (#coding:...) to use the
   correct encoding