diff --git a/lib/rack/livereload.rb b/lib/rack/livereload.rb
index 6ff2f04..4323f74 100644
--- a/lib/rack/livereload.rb
+++ b/lib/rack/livereload.rb
@@ -91,6 +91,9 @@ module Rack
           end
         end
 
+        body.close if body.respond_to?(:close)
+        new_body.close if new_body.respond_to?(:close)
+
         [ status, headers, new_body ]
       end
     end