Abstract: Container closure apparatus includes a rigid container having an open end with a top edge along with a a collapsible container disposed within the rigid container and having an open end. A cap is provided for covering the rigid and flexible container open ends and a plug seal provides a primary seal between the rigid container and the flexible container. The plug seal includes, in combination, a peripheral outwardly extending wall portion on the flexible container and a depending portion, extending from the cap, for pressing the wall portion against an inside wall of the rigid container. A gasket seal provides a secondary seal between the rigid container and the flexible container. The gasket seal includes, in combination, a lip outwardly extending from the flexible container open end and a groove, disposed in the cap, for pressing the lip against the rigid container top edge.