diff --git a/Lib/asyncore.py b/Lib/asyncore.py
--- a/Lib/asyncore.py
+++ b/Lib/asyncore.py
@@ -102,15 +102,17 @@
     except:
         obj.handle_error()
 
-def readwrite(obj, flags):
+def readwrite(obj, flags, map=None):
+    # 'map' may be None for backward compatibility
     try:
-        if flags & select.POLLIN:
+        if (not map or obj._fileno in map) and flags & select.POLLIN:
             obj.handle_read_event()
-        if flags & select.POLLOUT:
+        if (not map or obj._fileno in map) and flags & select.POLLOUT:
             obj.handle_write_event()
-        if flags & select.POLLPRI:
+        if (not map or obj._fileno in map) and flags & select.POLLPRI:
             obj.handle_expt_event()
-        if flags & (select.POLLHUP | select.POLLERR | select.POLLNVAL):
+        if ((not map or obj._fileno in map) and
+                    flags & (select.POLLHUP|select.POLLERR|select.POLLNVAL)):
             obj.handle_close()
     except socket.error as e:
         if e.args[0] not in _DISCONNECTED:
@@ -190,7 +192,7 @@
             obj = map.get(fd)
             if obj is None:
                 continue
-            readwrite(obj, flags)
+            readwrite(obj, flags, map)
 
 poll3 = poll2                           # Alias for backward compatibility
 
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
@@ -610,17 +610,25 @@
 
     def test_handle_close(self):
         # make sure handle_close is called when the other end closes
-        # the connection
+        # the connection, and that it is closed only once
 
         class TestClient(BaseClient):
 
+            def __init__(self, family, address):
+                BaseClient.__init__(self, family, address)
+                self.count = 0
+
             def handle_read(self):
                 # in order to make handle_close be called we are supposed
                 # to make at least one recv() call
                 self.recv(1024)
 
             def handle_close(self):
-                self.flag = True
+                self.count += 1
+                if self.count == 1:
+                    self.flag = True
+                else:
+                    self.flag = False
                 self.close()
 
         class TestHandler(BaseTestHandler):