diff --git a/Doc/library/enum.rst b/Doc/library/enum.rst
index 118002bef19f85..a9584b9c91083c 100644
--- a/Doc/library/enum.rst
+++ b/Doc/library/enum.rst
@@ -1164,6 +1164,15 @@ and raise an error if the two do not match::
     In Python 2 code the :attr:`_order_` attribute is necessary as definition
     order is lost before it can be recorded.
 
+
+_Private__names
+"""""""""""""""
+
+Private names are not converted to Enum members, but remain normal attributes.
+
+.. versionchanged:: 3.10
+
+
 ``Enum`` member type
 """"""""""""""""""""
 
diff --git a/Lib/enum.py b/Lib/enum.py
index f6c7e8b2334139..c130efccdc81dc 100644
--- a/Lib/enum.py
+++ b/Lib/enum.py
@@ -41,6 +41,19 @@ def _is_sunder(name):
             name[-2:-1] != '_'
             )
 
+def _is_private(cls_name, name):
+    # do not use `re` as `re` imports `enum`
+    pattern = '_%s__' % (cls_name, )
+    if (
+            len(name) >= 5
+            and name.startswith(pattern)
+            and name[len(pattern)] != '_'
+            and (name[-1] != '_' or name[-2] != '_')
+        ):
+        return True
+    else:
+        return False
+
 def _make_class_unpicklable(cls):
     """
     Make the given class un-picklable.
@@ -81,7 +94,10 @@ def __setitem__(self, key, value):
 
         Single underscore (sunder) names are reserved.
         """
-        if _is_sunder(key):
+        if _is_private(self._cls_name, key):
+            # do nothing, name will be a normal attribute
+            pass
+        elif _is_sunder(key):
             if key not in (
                     '_order_', '_create_pseudo_member_',
                     '_generate_next_value_', '_missing_', '_ignore_',
@@ -149,6 +165,7 @@ def __prepare__(metacls, cls, bases):
         metacls._check_for_existing_members(cls, bases)
         # create the namespace dict
         enum_dict = _EnumDict()
+        enum_dict._cls_name = cls
         # inherit previous flags and _generate_next_value_ function
         member_type, first_enum = metacls._get_mixins_(cls, bases)
         if first_enum is not None:
diff --git a/Lib/test/test_enum.py b/Lib/test/test_enum.py
index ab4b52f7852730..7138cc172e6bd9 100644
--- a/Lib/test/test_enum.py
+++ b/Lib/test/test_enum.py
@@ -1149,6 +1149,7 @@ def test_multiple_mixin_mro(self):
         class auto_enum(type(Enum)):
             def __new__(metacls, cls, bases, classdict):
                 temp = type(classdict)()
+                temp._cls_name = cls
                 names = set(classdict._member_names)
                 i = 0
                 for k in classdict._member_names:
@@ -2118,6 +2119,30 @@ class ThirdFailedStrEnum(StrEnum):
                 one = '1'
                 two = b'2', 'ascii', 9
 
+    @unittest.skipUnless(
+            sys.version_info[:2] == (3, 9),
+            'private variables are now normal attributes',
+            )
+    def test_warning_for_private_variables(self):
+        with self.assertWarns(DeprecationWarning):
+            class Private(Enum):
+                __corporal = 'Radar'
+        self.assertEqual(Private._Private__corporal.value, 'Radar')
+        try:
+            with self.assertWarns(DeprecationWarning):
+                class Private(Enum):
+                    __major_ = 'Hoolihan'
+        except ValueError:
+            pass
+
+    def test_private_variable_is_normal_attribute(self):
+        class Private(Enum):
+            __corporal = 'Radar'
+            __major_ = 'Hoolihan'
+        self.assertEqual(Private._Private__corporal, 'Radar')
+        self.assertEqual(Private._Private__major_, 'Hoolihan')
+
+
 class TestOrder(unittest.TestCase):
 
     def test_same_members(self):
diff --git a/Misc/NEWS.d/next/Library/2020-12-09-10-59-16.bpo-42517.FKEVcZ.rst b/Misc/NEWS.d/next/Library/2020-12-09-10-59-16.bpo-42517.FKEVcZ.rst
new file mode 100644
index 00000000000000..813139dfe5d005
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-12-09-10-59-16.bpo-42517.FKEVcZ.rst
@@ -0,0 +1,2 @@
+Enum: private names do not become members / do not generate errors -- they
+remain normal attributes