diff --git a/apisix/plugins/hmac-auth.lua b/apisix/plugins/hmac-auth.lua
index 905318ed0dde..e216d06ccfdb 100644
--- a/apisix/plugins/hmac-auth.lua
+++ b/apisix/plugins/hmac-auth.lua
@@ -330,7 +330,7 @@ function _M.rewrite(conf, ctx)
             return 401, err
         end
         core.log.warn(err)
-        return 401, {message = "client request can't be validated: " .. err}
+        return 401, {message = err}
     end
 
     if conf.hide_credentials then
diff --git a/apisix/plugins/jwt-auth.lua b/apisix/plugins/jwt-auth.lua
index 23b92ce07386..ae40c800b94c 100644
--- a/apisix/plugins/jwt-auth.lua
+++ b/apisix/plugins/jwt-auth.lua
@@ -237,8 +237,8 @@ function _M.rewrite(conf, ctx)
     local jwt_obj = jwt:load_jwt(jwt_token)
     core.log.info("jwt object: ", core.json.delay_encode(jwt_obj))
     if not jwt_obj.valid then
+        err = "JWT token invalid: " .. jwt_obj.reason
         if auth_utils.is_running_under_multi_auth(ctx) then
-            err = "JWT token invalid: " .. jwt_obj.reason
             return 401, err
         end
         core.log.warn(err)