A self-closing closure for use with a container, the closure opening automatically upon the application of opening pressure to the contents of the container and being self-closing upon the release of pressure. A pair of resilient discs or diaphragms are employed which in the closed position have their convex surfaces facing each other. One of these discs carries the valve opening and the other disc supports the valve stem which projects into and seals the opening in the closed position of the closure. Upon the application of opening pressure to the container contents, the resilient discs move axially of the closure and the convex surfaces change to concave surfaces. The valve stem is drawn away from the opening. The large axial movement of the discs is attained with minimal pressure yet secures a large opening area for dispensing the contents.