diff -r b6ea3dc89a78 Lib/unittest/mock.py
--- a/Lib/unittest/mock.py	Sat Jan 17 18:46:10 2015 +0200
+++ b/Lib/unittest/mock.py	Thu Jan 22 11:06:39 2015 +0200
@@ -2120,7 +2120,8 @@
         # descriptors don't have a spec
         # because we don't know what type they return
         _kwargs = {}
-    elif not _callable(spec):
+    elif not _callable(spec) and not isinstance(spec, (classmethod,
+                                                       staticmethod)):
         Klass = NonCallableMagicMock
     elif is_type and instance and not _instance_callable(spec):
         Klass = NonCallableMagicMock
diff -r b6ea3dc89a78 Lib/unittest/test/testmock/testmock.py
--- a/Lib/unittest/test/testmock/testmock.py	Sat Jan 17 18:46:10 2015 +0200
+++ b/Lib/unittest/test/testmock/testmock.py	Thu Jan 22 11:06:39 2015 +0200
@@ -1187,6 +1187,18 @@
         m = mock.create_autospec(object(), name='sweet_func')
         self.assertIn('sweet_func', repr(m))
 
+    #Issue23078
+    def test_create_autospec_classmethod_staticmethod(self):
+        funcs = [
+            staticmethod(lambda obj: obj),
+            classmethod(lambda obj: obj),
+        ]
+
+        for func in funcs:
+            func_mock = mock.create_autospec(func)
+            func_mock(2, 3)
+            self.assertEqual(func_mock.mock_calls, [call(2, 3)])
+
     #Issue21238
     def test_mock_unsafe(self):
         m = Mock()
diff -r b6ea3dc89a78 Lib/unittest/test/testmock/testpatch.py
--- a/Lib/unittest/test/testmock/testpatch.py	Sat Jan 17 18:46:10 2015 +0200
+++ b/Lib/unittest/test/testmock/testpatch.py	Thu Jan 22 11:06:39 2015 +0200
@@ -50,6 +50,14 @@
         pass
     foo = 'bar'
 
+    @staticmethod
+    def a_static():
+        return 24
+
+    @classmethod
+    def a_class(cls):
+        return 42
+
     class Bar(object):
         def a(self):
             pass
@@ -991,6 +999,16 @@
         self.assertEqual(result, 3)
 
 
+    def test_autospec_static_class_method(self):
+        with patch('%s.Foo.a_static' % __name__, autospec=True) as static:
+            static(24)
+            self.assertEqual(static.mock_calls, [call(24)])
+
+        with patch('%s.Foo.a_class' % __name__, autospec=True) as clsmethod:
+            clsmethod(42)
+            self.assertEqual(clsmethod.mock_calls, [call(42)])
+
+
     def test_autospec_with_new(self):
         patcher = patch('%s.function' % __name__, new=3, autospec=True)
         self.assertRaises(TypeError, patcher.start)