diff --git a/moto/apigateway/responses.py b/moto/apigateway/responses.py
index 37d6378a0..30fed63cd 100644
--- a/moto/apigateway/responses.py
+++ b/moto/apigateway/responses.py
@@ -2,6 +2,7 @@ from __future__ import unicode_literals
 
 import json
 
+from moto.utilities.utils import merge_multiple_dicts
 from moto.core.responses import BaseResponse
 from .models import apigateway_backends
 from .exceptions import (
@@ -363,6 +364,24 @@ class APIGatewayResponse(BaseResponse):
 
         return 200, {}, json.dumps(stage_response)
 
+    def restapis_stages_tags(self, request, full_url, headers):
+        self.setup_class(request, full_url, headers)
+        url_path_parts = self.path.split("/")
+        function_id = url_path_parts[4]
+        stage_name = url_path_parts[6]
+        if self.method == "PUT":
+            tags = self._get_param("tags")
+            if tags:
+                stage = self.backend.get_stage(function_id, stage_name)
+                stage["tags"] = merge_multiple_dicts(stage.get("tags"), tags)
+            return 200, {}, json.dumps({"item": tags})
+        if self.method == "DELETE":
+            stage = self.backend.get_stage(function_id, stage_name)
+            for tag in stage.get("tags").copy():
+                if tag in self.querystring.get("tagKeys"):
+                    stage["tags"].pop(tag, None)
+            return 200, {}, json.dumps({"item": ""})
+
     def stages(self, request, full_url, headers):
         self.setup_class(request, full_url, headers)
         url_path_parts = self.path.split("/")
diff --git a/moto/apigateway/urls.py b/moto/apigateway/urls.py
index 5d0271f65..b6cc567a3 100644
--- a/moto/apigateway/urls.py
+++ b/moto/apigateway/urls.py
@@ -12,6 +12,7 @@ url_paths = {
     "{0}/restapis/(?P<function_id>[^/]+)/authorizers$": response.restapis_authorizers,
     "{0}/restapis/(?P<function_id>[^/]+)/authorizers/(?P<authorizer_id>[^/]+)/?$": response.authorizers,
     "{0}/restapis/(?P<function_id>[^/]+)/stages$": response.restapis_stages,
+    "{0}/tags/arn:aws:apigateway:(?P<region_name>[^/]+)::/restapis/(?P<function_id>[^/]+)/stages/(?P<stage_name>[^/]+)/?$": response.restapis_stages_tags,
     "{0}/restapis/(?P<function_id>[^/]+)/stages/(?P<stage_name>[^/]+)/?$": response.stages,
     "{0}/restapis/(?P<function_id>[^/]+)/deployments$": response.deployments,
     "{0}/restapis/(?P<function_id>[^/]+)/deployments/(?P<deployment_id>[^/]+)/?$": response.individual_deployment,
diff --git a/tests/terraform-tests.success.txt b/tests/terraform-tests.success.txt
index 1578b48fa..c916cdc6f 100644
--- a/tests/terraform-tests.success.txt
+++ b/tests/terraform-tests.success.txt
@@ -78,6 +78,9 @@ TestAccAWSUserPolicyAttachment
 TestAccAWSUserSSHKey
 TestAccAWSVpc_
 TestAccAWSRouteTable_disappears
+TestAccAWSAPIGatewayStage_basic
+TestAccAWSAPIGatewayStage_accessLogSettings_kinesis
+TestAccAWSAPIGatewayStage_accessLogSettings
 TestAccAWSRouteTable_RequireRouteTarget
 TestAccAWSRouteTable_Route_ConfigMode
 TestAccAWSRouteTable_tags