diff --git a/Lib/asyncore.py b/Lib/asyncore.py
--- a/Lib/asyncore.py
+++ b/Lib/asyncore.py
@@ -338,8 +338,14 @@
     def connect(self, address):
         self.connected = False
         err = self.socket.connect_ex(address)
-        if err in (EINPROGRESS, EALREADY, EWOULDBLOCK) \
-        or err == EINVAL and os.name in ('nt', 'ce'):
+        # connection being established asynchronously
+        if err in (EINPROGRESS, EWOULDBLOCK):
+            # EWOULDBLOCK may also be returned by winsock when calling connect
+            # while the connection attempt is in progress
+            if not self.addr:
+                self.addr = address
+            return
+        if (err == EALREADY or (err == EINVAL and os.name in ('nt', 'ce'))):
             return
         if err in (0, EISCONN):
             self.addr = address
diff --git a/Lib/test/test_asyncore.py b/Lib/test/test_asyncore.py
--- a/Lib/test/test_asyncore.py
+++ b/Lib/test/test_asyncore.py
@@ -777,6 +777,18 @@
         finally:
             sock.close()
 
+    def test_addr_after_connect(self):
+        # Check that 'addr' is not None after connect (issue #XXX)
+
+        class TestClient(BaseClient):
+            def handle_write(self):
+                if self.addr:
+                    self.flag = True
+
+        server = BaseServer(self.family, self.addr)
+        client = TestClient(self.family, server.address)
+        self.loop_waiting_for_flag(client)
+
 
 class TestAPI_UseIPv4Sockets(BaseTestAPI):
     family = socket.AF_INET