A closing apparatus for closing preferably bag-type packaging units by compression, which units have regions of differing thickness along the package opening to be closed, such as square bottom bags for instance, in particular made of coated or uncoated paper, paperboard, plastic, film, and/or woven material, which packaging units have at least one suitable sealing surface that is integrated in or applied to the material for permanent bonding to a surface that is adjacent to or opposite and pressed against the material, wherein the closing apparatus has a pressing device with at least one pressure device and at least one counter-pressure device between which the packaging units can be compressed, preferably with the application of heat, in the region of their sealing surface(s). In order to achieve a uniformly durable closure, the pressure device and the counter-pressure device have zones of different pressure and/or different temperature along the package opening to be closed.