A lid for closing containers includes an at least two-layered composite assembly. A layer facing the container seals against a container edge and forms an opening by layer separation, for removing contents. The layers have a continuous construction without weakening lines. The layer facing the container is made mainly of a plastic having an intrinsic tearing resistance being lower in the region of the opening than its adhesion to the layer facing away from the container in a remaining region and an adhesion to the container edge being greater at least in the region of an opening aid than to the other layer. The plastic adheres so strongly to the outer layer in the region of the opening that a region corresponding to the opening is torn out upon opening and a remaining layer of the lid facing the container continues to adhere to the container edge by sealing action.