diff --git a/Lib/test/support.py b/Lib/test/support.py
index 4e946aba2c6..801ecf2193d 100644
--- a/Lib/test/support.py
+++ b/Lib/test/support.py
@@ -677,7 +677,11 @@ elif sys.platform != 'darwin':
 # decoded from the filesystem encoding (in strict mode). It can be None if we
 # cannot generate such filename.
 TESTFN_UNDECODABLE = None
-for name in (b'abc\xff', b'\xe7w\xf0'):
+# b'\xff' is not decodable by os.fsdecode() with code page 932. Windows
+# accepts it to create a file or a directory, or don't accept to enter to
+# such directory (when the bytes name is used). So test b'\xe7' first: it is
+# not decodable from cp932.
+for name in (b'\xe7w\xf0', b'abc\xff'):
     try:
         os.fsdecode(name)
     except UnicodeDecodeError:
diff --git a/Lib/test/test_genericpath.py b/Lib/test/test_genericpath.py
index b1ee110e468..9d1d2bcc57b 100644
--- a/Lib/test/test_genericpath.py
+++ b/Lib/test/test_genericpath.py
@@ -308,17 +308,28 @@ class CommonTest(GenericTest):
                 for path in ('', 'fuu', 'f\xf9\xf9', '/fuu', 'U:\\'):
                     self.assertIsInstance(abspath(path), str)
 
-    @unittest.skipIf(sys.platform == 'darwin',
-        "Mac OS X denies the creation of a directory with an invalid utf8 name")
     def test_nonascii_abspath(self):
-        if support.TESTFN_UNDECODABLE:
-            name = support.TESTFN_UNDECODABLE
-        elif support.TESTFN_NONASCII:
-            name = support.TESTFN_NONASCII
+        # Test non-ASCII in the path
+        if sys.platform in ('win32', 'darwin'):
+            if support.TESTFN_NONASCII:
+                name = support.TESTFN_NONASCII
+            else:
+                # Mac OS X denies the creation of a directory with an invalid
+                # UTF-8 name. Windows allows to create a directory with an
+                # arbitrary bytes name, but fails to enter this directory
+                # (when the bytes name is used).
+                self.skipTest("need support.TESTFN_NONASCII")
         else:
-            name = b'a\xffb\xe7w\xf0'
+            if support.TESTFN_UNDECODABLE:
+                name = support.TESTFN_UNDECODABLE
+            elif support.TESTFN_NONASCII:
+                name = support.TESTFN_NONASCII
+            else:
+                # On UNIX, the surrogateescape error handler is used to
+                # decode paths, so any byte is allowed, it does not depend
+                # on the locale
+                name = b'a\xffb\xe7w\xf0'
 
-        # Test non-ASCII, non-UTF8 bytes in the path.
         with warnings.catch_warnings():
             warnings.simplefilter("ignore", DeprecationWarning)
             with support.temp_cwd(name):