The invention relates to a closing system for containers for storing or administering liquid, pasty or powdery materials, consisting of a cap (81, 82) provided with a through-hole (85) and a closing element (60), the cap holding the closing element on the container (10, 50) in a non-positive or positive manner, in the region of the opening (12) to be closed, by means of a rear grip (37) on the container. To this end, the front surface (21) surrounding the container opening and on which the closing element is arranged comprises a recess (24, 25). The closing element is a virus-tight, bacteria-tight and spore-tight film which lies on the front surface and at least partially over the recess. An elastomer or adhesive ring (71, 72) filling the recess is arranged between the closing element and the recess for the positioning of the cap. The invention provides a closing system for containers which enables the container to be closed in a virus-tight, bacteria-tight, spore-tight and lastingly secure manner.