diff --git a/ircstream/ircserver.py b/ircstream/ircserver.py
index f98bdf3..b974d65 100644
--- a/ircstream/ircserver.py
+++ b/ircstream/ircserver.py
@@ -30,6 +30,8 @@
 
 from ._version import __version__
 
+MESSAGE_QUEUE_SIZE = 1000  # maximum number of messages that will be queued for each client
+
 logger = structlog.get_logger()
 
 
@@ -216,6 +218,7 @@ def __init__(self, server: IRCServer, reader: asyncio.StreamReader, writer: asyn
         self.host: str = ""
         self.port: int = 0
         self._background_tasks: set[asyncio.Task[Any]] = set()
+        self._bot_message_queue: asyncio.Queue[tuple[str, str]] = asyncio.Queue(maxsize=MESSAGE_QUEUE_SIZE)
 
     def create_background_task(self, coro: Coroutine[Any, Any, None]) -> None:
         """Spawn a background attached to this client."""
@@ -236,6 +239,7 @@ async def connect(self) -> None:
         self.server.metrics["clients"].inc()
 
         self.create_background_task(self._periodic_ping())
+        self.create_background_task(self._bot_message_queue_processor())
         await self._handle_forever()
 
     async def terminate(self) -> None:
@@ -264,6 +268,27 @@ async def _periodic_ping(self) -> None:
             if self.registered:
                 await self.msg("PING", self.server.servername)
 
+    def enqueue_bot_message(self, target: str, msg: str) -> None:
+        """Add a message to the queue of pending bot messages.
+
+        Will never block. May raise asyncio.QueueFull if this client's queue is full.
+
+        Typically called from IRCServer.broadcast().
+        """
+        return self._bot_message_queue.put_nowait((target, msg))
+
+    async def _bot_message_queue_processor(self) -> None:
+        """Process the bot message queue continuously."""
+        while True:
+            target, msg = await self._bot_message_queue.get()  # blocks until there is a queued item
+            try:
+                await self.msg("PRIVMSG", [target, msg], from_bot=True)
+            except Exception:
+                self.server.metrics["errors"].labels("broadcast_send").inc()
+                self.log.debug("Unable to dequeue broadcast", exc_info=True)
+            finally:
+                self._bot_message_queue.task_done()
+
     async def msg(self, command: str | IRCNumeric, params: list[str] | str, from_bot: bool = False) -> None:
         """Prepare and sends a response to the client.
 
@@ -842,9 +867,13 @@ async def broadcast(self, target: str, msg: str) -> None:
         clients = self._channels.setdefault(target, set())
         for client in clients:
             try:
-                await client.msg("PRIVMSG", [target, msg], from_bot=True)
+                client.enqueue_bot_message(target, msg)
+            except asyncio.QueueFull:
+                self.metrics["errors"].labels("queue_overrun").inc()
+                self.log.debug("Client queue overrun", client=client.internal_ident)
+                continue  # client is losing messages, but other clients should not suffer
             except Exception:
-                self.metrics["errors"].labels("broadcast").inc()
-                self.log.debug("Unable to broadcast", exc_info=True)
-                continue  # ignore exceptions, to catch corner cases
+                self.metrics["errors"].labels("broadcast_enqueue").inc()
+                self.log.warning("Unable to enqueue broadcast", client=client.internal_ident, exc_info=True)
+                continue  # ignore all exceptions, to catch corner cases
         self.metrics["messages"].inc()