diff -r 44f455e6163d Lib/argparse.py
--- a/Lib/argparse.py	Thu Jun 27 12:23:29 2013 +0200
+++ b/Lib/argparse.py	Fri Jul 25 22:46:41 2014 -0700
@@ -1544,6 +1544,9 @@
         super(_ArgumentGroup, self)._remove_action(action)
         self._group_actions.remove(action)
 
+    def add_argument_group(self, *args, **kwargs):
+        raise ValueError('Cannot nest groups')
+
 
 class _MutuallyExclusiveGroup(_ArgumentGroup):
 
@@ -1564,6 +1567,9 @@
         self._container._remove_action(action)
         self._group_actions.remove(action)
 
+    def add_mutually_exclusive_group(self, **kwargs):
+        raise ValueError('Cannot nest mutually exclusive groups')
+
 
 class ArgumentParser(_AttributeHolder, _ActionsContainer):
     """Object for parsing command line strings into Python objects.
diff -r 44f455e6163d Lib/test/test_argparse.py
--- a/Lib/test/test_argparse.py	Thu Jun 27 12:23:29 2013 +0200
+++ b/Lib/test/test_argparse.py	Fri Jul 25 22:46:41 2014 -0700
@@ -2326,6 +2326,15 @@
               '''
         self.assertEqual(parser.format_help(), textwrap.dedent(expected))
 
+    def test_invalid_add_group(self):
+        parser = ErrorRaisingArgumentParser()
+        group = parser.add_mutually_exclusive_group()
+        add_group = group.add_mutually_exclusive_group
+        raises = self.assertRaises
+        raises(ValueError, group.add_mutually_exclusive_group)
+        raises(ValueError, group.add_argument_group, 'title')
+
+
 class MEMixin(object):
 
     def test_failures_when_not_required(self):