Abstract: Closure membrane for containers having an outer film and inner film with a joining layer and a sealing seam zone between these two films. At least one space free of a bonding layer is provided within the sealing seam zone between the outer film and the inner film and, within the limits of this non-bonded space, the outer film and the inner film each feature at least one opening, and a reservoir of material that softens under the influence of heat is provided in the non-bonded space between the outer film and the inner film. The openings in the inner film and the openings in the outer film are connected to enable the passage of a fluid such as a gas from the interior of the container to the surrounding atmosphere. On application of heat to the closure membrane e.g. during a sterilization process, the openings in the inner film and the outer film are closed off as a result of softening of the material that softens under the influence of heat.