diff --git a/CHANGES b/CHANGES
index d27b6cd07..10bf627fb 100644
--- a/CHANGES
+++ b/CHANGES
@@ -58,6 +58,8 @@ Bugs fixed
   declarations.
 * C++, suppress warnings for directly dependent typenames in cross references
   generated automatically in signatures.
+* #5637: autodoc: Incorrect handling of nested class names on show-inheritance
+* #5637: inheritance_diagram: Incorrect handling of nested class names
 
 Testing
 --------
diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index b9404804b..ae56cb183 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -1146,7 +1146,7 @@ class ClassDocumenter(DocstringSignatureMixin, ModuleLevelDocumenter):  # type:
             if hasattr(self.object, '__bases__') and len(self.object.__bases__):
                 bases = [':class:`%s`' % b.__name__
                          if b.__module__ in ('__builtin__', 'builtins')
-                         else ':class:`%s.%s`' % (b.__module__, b.__name__)
+                         else ':class:`%s.%s`' % (b.__module__, b.__qualname__)
                          for b in self.object.__bases__]
                 self.add_line('   ' + _('Bases: %s') % ', '.join(bases),
                               sourcename)
diff --git a/sphinx/ext/inheritance_diagram.py b/sphinx/ext/inheritance_diagram.py
index 83e277523..db2a15b14 100644
--- a/sphinx/ext/inheritance_diagram.py
+++ b/sphinx/ext/inheritance_diagram.py
@@ -229,7 +229,7 @@ class InheritanceGraph:
         if module in ('__builtin__', 'builtins'):
             fullname = cls.__name__
         else:
-            fullname = '%s.%s' % (module, cls.__name__)
+            fullname = '%s.%s' % (module, cls.__qualname__)
         if parts == 0:
             result = fullname
         else:
diff --git a/tests/roots/test-ext-autodoc/target/__init__.py b/tests/roots/test-ext-autodoc/target/__init__.py
index f6970a36c..e28eeef8a 100644
--- a/tests/roots/test-ext-autodoc/target/__init__.py
+++ b/tests/roots/test-ext-autodoc/target/__init__.py
@@ -110,6 +110,10 @@ class Outer(object):
     factory = dict
 
 
+class InnerChild(Outer.Inner):
+    """InnerChild docstring"""
+
+
 class DocstringSig(object):
     def meth(self):
         """meth(FOO, BAR=1) -> BAZ
diff --git a/tests/roots/test-inheritance/diagram_w_nested_classes.rst b/tests/roots/test-inheritance/diagram_w_nested_classes.rst
new file mode 100644
index 000000000..7fa02175f
--- /dev/null
+++ b/tests/roots/test-inheritance/diagram_w_nested_classes.rst
@@ -0,0 +1,5 @@
+Diagram with Nested Classes
+===========================
+
+.. inheritance-diagram::
+    dummy.test_nested
diff --git a/tests/roots/test-inheritance/dummy/test_nested.py b/tests/roots/test-inheritance/dummy/test_nested.py
new file mode 100644
index 000000000..1e732aab5
--- /dev/null
+++ b/tests/roots/test-inheritance/dummy/test_nested.py
@@ -0,0 +1,12 @@
+"""
+    Test with nested classes.
+"""
+
+
+class A(object):
+    class B(object):
+        pass
+
+
+class C(A.B):
+    pass
diff --git a/tests/test_autodoc.py b/tests/test_autodoc.py
index 52e9bf5c5..e6b4cc5b6 100644
--- a/tests/test_autodoc.py
+++ b/tests/test_autodoc.py
@@ -685,6 +685,7 @@ def test_autodoc_ignore_module_all(app):
     assert list(filter(lambda l: 'class::' in l, actual)) == [
         '.. py:class:: Class(arg)',
         '.. py:class:: CustomDict',
+        '.. py:class:: InnerChild',
         '.. py:class:: InstAttCls()',
         '.. py:class:: Outer',
         '   .. py:class:: Outer.Inner',
@@ -775,6 +776,18 @@ def test_autodoc_inner_class(app):
         '      ',
     ]
 
+    options['show-inheritance'] = True
+    actual = do_autodoc(app, 'class', 'target.InnerChild', options)
+    assert list(actual) == [
+        '',
+        '.. py:class:: InnerChild',
+        '   :module: target', '',
+        '   Bases: :class:`target.Outer.Inner`',
+        '',
+        '   InnerChild docstring',
+        '   '
+    ]
+
 
 @pytest.mark.sphinx('html', testroot='ext-autodoc')
 def test_autodoc_classmethod(app):
diff --git a/tests/test_ext_inheritance_diagram.py b/tests/test_ext_inheritance_diagram.py
index baeaa401e..3125f2c6e 100644
--- a/tests/test_ext_inheritance_diagram.py
+++ b/tests/test_ext_inheritance_diagram.py
@@ -132,6 +132,14 @@ def test_inheritance_diagram(app, status, warning):
             ('dummy.test.A', 'dummy.test.A', [], None),
         ]
 
+    # inheritance diagram involving a base class nested within another class
+    for cls in graphs['diagram_w_nested_classes'].class_info:
+        assert cls in [
+            ('dummy.test_nested.A', 'dummy.test_nested.A', [], None),
+            ('dummy.test_nested.C', 'dummy.test_nested.C', ['dummy.test_nested.A.B'], None),
+            ('dummy.test_nested.A.B', 'dummy.test_nested.A.B', [], None)
+        ]
+
 
 @pytest.mark.sphinx('html', testroot='ext-inheritance_diagram')
 @pytest.mark.usefixtures('if_graphviz_found')