The bottle-shaped container is made in a coextrusion blow molding process and has a dimensionally stable outer container and an easily deformable inner bag which consist of different thermoplastic materials that cannot be welded to each other. The preform has a diameter greater than that of the bottle neck so that, when the blow mold is closed, the blow mold halves squeeze off excess material not only on the bottom, but also in the shoulder and neck area. Unwelded seams of the outer container are thereby formed in the shoulder and neck area. In the bottom area the outer container is closed by a weld seam which has been formed by displacing material, the weld seam of the inner bag being fixed in said area. After negative pressure has been applied to the inner bag, holes are formed in the upper area of the outer container for the purpose of a permanent pressure compensation. All openings in the outer container are covered by the pump housing. The container operates reliably in the upside-down position.