diff --git a/Lib/multiprocessing/connection.py b/Lib/multiprocessing/connection.py
index 463d472..645a26f 100644
--- a/Lib/multiprocessing/connection.py
+++ b/Lib/multiprocessing/connection.py
@@ -285,9 +285,13 @@
         return conn
 
     def close(self):
-        self._socket.close()
-        if self._unlink is not None:
-            self._unlink()
+        try:
+            self._socket.close()
+        finally:
+            unlink = self._unlink
+            if unlink is not None:
+                self._unlink = None
+                unlink()
 
 
 def SocketClient(address):
diff --git a/Lib/multiprocessing/queues.py b/Lib/multiprocessing/queues.py
index 487e0af..a88e298 100644
--- a/Lib/multiprocessing/queues.py
+++ b/Lib/multiprocessing/queues.py
@@ -156,9 +156,13 @@
 
     def close(self):
         self._closed = True
-        self._reader.close()
-        if self._close:
-            self._close()
+        try:
+            self._reader.close()
+        finally:
+            close = self._close
+            if close:
+                self._close = None
+                close()
 
     def join_thread(self):
         debug('Queue.join_thread()')