diff --git a/moto/autoscaling/models.py b/moto/autoscaling/models.py
index d54c39d71..a47eac779 100644
--- a/moto/autoscaling/models.py
+++ b/moto/autoscaling/models.py
@@ -440,6 +440,13 @@ class AutoScalingBackend(BaseBackend):
             self.elb_backend.register_instances(elb.name, group_instance_ids - elb_instace_ids)
             self.elb_backend.deregister_instances(elb.name, elb_instace_ids - group_instance_ids)
 
+    def create_or_update_tags(self, tags):
+        for tag in tags:
+            group_name = tag["ResourceId"]
+            group = self.autoscaling_groups[group_name]
+            updated_tags = group.tags.copy()
+            updated_tags.update(tag)
+            group.tags = updated_tags
 
 autoscaling_backends = {}
 for region, ec2_backend in ec2_backends.items():
diff --git a/moto/autoscaling/responses.py b/moto/autoscaling/responses.py
index 79cb6aeee..b3ec57f27 100644
--- a/moto/autoscaling/responses.py
+++ b/moto/autoscaling/responses.py
@@ -105,6 +105,11 @@ class AutoScalingResponse(BaseResponse):
         template = self.response_template(SET_DESIRED_CAPACITY_TEMPLATE)
         return template.render()
 
+    def create_or_update_tags(self):
+        tags = self._get_param('Tags')
+        self.autoscaling_backend.create_or_update_tags(tags)
+        return None
+
     def describe_auto_scaling_instances(self):
         instance_states = self.autoscaling_backend.describe_autoscaling_instances()
         template = self.response_template(DESCRIBE_AUTOSCALING_INSTANCES_TEMPLATE)