diff --git a/channels/delay/models.py b/channels/delay/models.py
index 4bff090..932d6d3 100644
--- a/channels/delay/models.py
+++ b/channels/delay/models.py
@@ -30,15 +30,20 @@ class DelayedMessage(models.Model):
         self._delay = milliseconds
         self.due_date = timezone.now() + timedelta(milliseconds=milliseconds)
 
-    def send(self, channel_layer=None):
+    def send(self, channel_layer=None, requeue_delay=1000):
         """
         Sends the message on the configured channel with the stored content.
 
-        Deletes the DelayedMessage record.
+        Deletes the DelayedMessage record if successfully sent.
 
         Args:
             channel_layer: optional channel_layer to use
+            requeue_delay: if the channel is full, milliseconds to wait before requeue
         """
         channel_layer = channel_layer or channel_layers[DEFAULT_CHANNEL_LAYER]
-        Channel(self.channel_name, channel_layer=channel_layer).send(json.loads(self.content), immediately=True)
-        self.delete()
+        try:
+            Channel(self.channel_name, channel_layer=channel_layer).send(json.loads(self.content), immediately=True)
+            self.delete()
+        except channel_layer.ChannelFull:
+            self.delay = requeue_delay
+            self.save()
diff --git a/tests/test_delay.py b/tests/test_delay.py
index 08cb194..a6de9dd 100644
--- a/tests/test_delay.py
+++ b/tests/test_delay.py
@@ -71,6 +71,41 @@ class WorkerTests(ChannelTestCase):
         message = self.get_next_message('test', require=True)
         self.assertEqual(message.content, {'test': 'value'})
 
+    def test_channel_full(self):
+        """
+        Tests that when channel capacity is hit when processing due messages,
+        message is requeued instead of dropped
+        """
+        for i in range(10):
+            Channel('asgi.delay').send({
+                'channel': 'test',
+                'delay': 1000,
+                'content': {'test': 'value'}
+            }, immediately=True)
+
+        worker = PatchedWorker(channel_layers[DEFAULT_CHANNEL_LAYER])
+        worker.termed = 10
+        worker.run()
+
+        for i in range(1):
+            Channel('asgi.delay').send({
+                'channel': 'test',
+                'delay': 1000,
+                'content': {'test': 'value'}
+            }, immediately=True)
+
+        worker = PatchedWorker(channel_layers[DEFAULT_CHANNEL_LAYER])
+        worker.termed = 1
+        worker.run()
+
+        self.assertEqual(DelayedMessage.objects.count(), 11)
+
+        with mock.patch('django.utils.timezone.now', return_value=timezone.now() + timedelta(milliseconds=2000)):
+            worker.termed = 1
+            worker.run()
+
+        self.assertEqual(DelayedMessage.objects.count(), 1)
+
 
 class DelayedMessageTests(ChannelTestCase):