diff --git a/Lib/test/test_tokenize.py b/Lib/test/test_tokenize.py
--- a/Lib/test/test_tokenize.py
+++ b/Lib/test/test_tokenize.py
@@ -594,6 +594,20 @@ def"', """\
     STRING     "'green'"     (2, 7) (2, 14)
     """)
 
+        self.check_tokenize("℘· = 1\n℮᧚ = 2\n℮··፩፰፱᧚ = 3", """\
+    NAME       '℘·'          (1, 0) (1, 2)
+    OP         '='           (1, 3) (1, 4)
+    NUMBER     '1'           (1, 5) (1, 6)
+    NEWLINE    '\\n'          (1, 6) (1, 7)
+    NAME       '℮᧚'          (2, 0) (2, 2)
+    OP         '='           (2, 3) (2, 4)
+    NUMBER     '2'           (2, 5) (2, 6)
+    NEWLINE    '\\n'          (2, 6) (2, 7)
+    NAME       '℮··፩፰፱᧚'     (3, 0) (3, 7)
+    OP         '='           (3, 8) (3, 9)
+    NUMBER     '3'           (3, 10) (3, 11)
+    """)
+
     def test_unicode(self):
         # Legacy unicode literals:
         self.check_tokenize("Örter = u'places'\ngrün = U'green'", """\
diff --git a/Lib/tokenize.py b/Lib/tokenize.py
--- a/Lib/tokenize.py
+++ b/Lib/tokenize.py
@@ -118,7 +118,9 @@ def maybe(*choices): return group(*choic
 Whitespace = r'[ \f\t]*'
 Comment = r'#[^\r\n]*'
 Ignore = Whitespace + any(r'\\\r?\n' + Whitespace) + maybe(Comment)
-Name = r'\w+'
+IDStart = group(r'\w', r'[\u2118\u212E\u309B\u309C]')
+IDContinue = group(IDStart, r'[\u00B7\u0387\u1369-\u1371\u19DA]')
+Name = IDStart + any(IDContinue)
 
 Hexnumber = r'0[xX][0-9a-fA-F]+'
 Binnumber = r'0[bB][01]+'