diff --git a/Lib/asyncio/base_events.py b/Lib/asyncio/base_events.py
index c58906f..9613ac2 100644
--- a/Lib/asyncio/base_events.py
+++ b/Lib/asyncio/base_events.py
@@ -1306,7 +1306,8 @@
                     if local_addr:
                         sock.bind(local_address)
                     if remote_addr:
-                        await self.sock_connect(sock, remote_address)
+                        if not allow_broadcast:
+                            await self.sock_connect(sock, remote_address)
                         r_addr = remote_address
                 except OSError as exc:
                     if sock is not None:
diff --git a/Lib/asyncio/selector_events.py b/Lib/asyncio/selector_events.py
index 93b6889..2996821 100644
--- a/Lib/asyncio/selector_events.py
+++ b/Lib/asyncio/selector_events.py
@@ -587,7 +587,10 @@
     def __init__(self, loop, sock, protocol, extra=None, server=None):
         super().__init__(extra, loop)
         self._extra['socket'] = sock
-        self._extra['sockname'] = sock.getsockname()
+        try:
+            self._extra['sockname'] = sock.getsockname()
+        except OSError:
+            self._extra['sockname'] = None
         if 'peername' not in self._extra:
             try:
                 self._extra['peername'] = sock.getpeername()
@@ -976,9 +979,11 @@
         if not data:
             return
 
-        if self._address and addr not in (None, self._address):
-            raise ValueError(
-                f'Invalid address: must be None or {self._address}')
+        if self._address:
+            if addr not in (None, self._address):
+                raise ValueError(
+                    f'Invalid address: must be None or {self._address}')
+            addr = self._address
 
         if self._conn_lost and self._address:
             if self._conn_lost >= constants.LOG_THRESHOLD_FOR_CONNLOST_WRITES:
@@ -989,7 +994,7 @@
         if not self._buffer:
             # Attempt to send it right away first.
             try:
-                if self._address:
+                if self._extra['peername']:
                     self._sock.send(data)
                 else:
                     self._sock.sendto(data, addr)
@@ -1012,7 +1017,7 @@
         while self._buffer:
             data, addr = self._buffer.popleft()
             try:
-                if self._address:
+                if self._extra['peername']:
                     self._sock.send(data)
                 else:
                     self._sock.sendto(data, addr)