diff --git a/winsup/cygwin/fhandler_socket_inet.cc b/winsup/cygwin/fhandler_socket_inet.cc
index 4ecb31a27..f6bb8c503 100644
--- a/winsup/cygwin/fhandler_socket_inet.cc
+++ b/winsup/cygwin/fhandler_socket_inet.cc
@@ -785,11 +785,13 @@ fhandler_socket_inet::connect (const struct sockaddr *name, int namelen)
   if (get_inet_addr_inet (name, namelen, &sst, &namelen) == SOCKET_ERROR)
     return SOCKET_ERROR;
 
-  /* Initialize connect state to "connect_pending".  State is ultimately set
-     to "connected" or "connect_failed" in wait_for_events when the FD_CONNECT
-     event occurs.  Note that the underlying OS sockets are always non-blocking
-     and a successfully initiated non-blocking Winsock connect always returns
-     WSAEWOULDBLOCK.  Thus it's safe to rely on event handling.
+  /* Initialize connect state to "connect_pending".  In the SOCK_STREAM
+     case, the state is ultimately set to "connected" or "connect_failed" in
+     wait_for_events when the FD_CONNECT event occurs.  Note that the
+     underlying OS sockets are always non-blocking in this case and a
+     successfully initiated non-blocking Winsock connect always returns
+     WSAEWOULDBLOCK.  Thus it's safe to rely on event handling.  For DGRAM
+     sockets, however, connect can return immediately.
 
      Check for either unconnected or connect_failed since in both cases it's
      allowed to retry connecting the socket.  It's also ok (albeit ugly) to
@@ -801,7 +803,9 @@ fhandler_socket_inet::connect (const struct sockaddr *name, int namelen)
     connect_state (connect_pending);
 
   int res = ::connect (get_socket (), (struct sockaddr *) &sst, namelen);
-  if (!is_nonblocking ()
+  if (!res)
+    connect_state (connected);
+  else if (!is_nonblocking ()
       && res == SOCKET_ERROR
       && WSAGetLastError () == WSAEWOULDBLOCK)
     res = wait_for_events (FD_CONNECT | FD_CLOSE, 0);
@@ -824,8 +828,7 @@ fhandler_socket_inet::connect (const struct sockaddr *name, int namelen)
 	 Convert to POSIX/Linux compliant EISCONN. */
       else if (err == WSAEINVAL && connect_state () == listener)
 	WSASetLastError (WSAEISCONN);
-      /* Any other error except WSAEALREADY during connect_pending means the
-         connect failed. */
+      /* Any other error except WSAEALREADY means the connect failed. */
       else if (connect_state () == connect_pending && err != WSAEALREADY)
 	connect_state (connect_failed);
       set_winsock_errno ();
diff --git a/winsup/cygwin/fhandler_socket_local.cc b/winsup/cygwin/fhandler_socket_local.cc
index ad7dd0a98..1c8d48b58 100644
--- a/winsup/cygwin/fhandler_socket_local.cc
+++ b/winsup/cygwin/fhandler_socket_local.cc
@@ -914,11 +914,13 @@ fhandler_socket_local::connect (const struct sockaddr *name, int namelen)
   if (get_socket_type () == SOCK_STREAM)
     af_local_set_cred ();
 
-  /* Initialize connect state to "connect_pending".  State is ultimately set
-     to "connected" or "connect_failed" in wait_for_events when the FD_CONNECT
-     event occurs.  Note that the underlying OS sockets are always non-blocking
-     and a successfully initiated non-blocking Winsock connect always returns
-     WSAEWOULDBLOCK.  Thus it's safe to rely on event handling.
+  /* Initialize connect state to "connect_pending".  In the SOCK_STREAM
+     case, the state is ultimately set to "connected" or "connect_failed" in
+     wait_for_events when the FD_CONNECT event occurs.  Note that the
+     underlying OS sockets are always non-blocking in this case and a
+     successfully initiated non-blocking Winsock connect always returns
+     WSAEWOULDBLOCK.  Thus it's safe to rely on event handling.  For DGRAM
+     sockets, however, connect can return immediately.
 
      Check for either unconnected or connect_failed since in both cases it's
      allowed to retry connecting the socket.  It's also ok (albeit ugly) to
@@ -930,7 +932,9 @@ fhandler_socket_local::connect (const struct sockaddr *name, int namelen)
     connect_state (connect_pending);
 
   int res = ::connect (get_socket (), (struct sockaddr *) &sst, namelen);
-  if (!is_nonblocking ()
+  if (!res)
+    connect_state (connected);
+  else if (!is_nonblocking ()
       && res == SOCKET_ERROR
       && WSAGetLastError () == WSAEWOULDBLOCK)
     res = wait_for_events (FD_CONNECT | FD_CLOSE, 0);
@@ -953,8 +957,7 @@ fhandler_socket_local::connect (const struct sockaddr *name, int namelen)
 	 Convert to POSIX/Linux compliant EISCONN. */
       else if (err == WSAEINVAL && connect_state () == listener)
 	WSASetLastError (WSAEISCONN);
-      /* Any other error except WSAEALREADY during connect_pending means the
-         connect failed. */
+      /* Any other error except WSAEALREADY means the connect failed. */
       else if (connect_state () == connect_pending && err != WSAEALREADY)
 	connect_state (connect_failed);
       set_winsock_errno ();
diff --git a/winsup/cygwin/release/3.2.1 b/winsup/cygwin/release/3.2.1
index c1ada5d50..7662c7114 100644
--- a/winsup/cygwin/release/3.2.1
+++ b/winsup/cygwin/release/3.2.1
@@ -12,7 +12,7 @@ Bug Fixes
 - Fix values returned by select(2) for shutdown sockets.
   Addresses: https://cygwin.com/pipermail/cygwin-developers/2021-April/012092.html
 
-- Introduce a new hypotl(3) function not suffering unnecesswry overflows.
+- Introduce a new hypotl(3) function not suffering unnecessary overflows.
   Addresses: https://cygwin.com/pipermail/cygwin/2021-April/248302.html
 
 - Fix path handling for paths spanning native symlinks.
@@ -25,3 +25,6 @@ Bug Fixes
 
 - Handle two race conditions in pseudo console usage.
   Addresses: https://cygwin.com/pipermail/cygwin/2021-April/248292.html
+
+- Fix a bug in recognizing a successful completion of connect(2) on a
+  datagram socket.