Elastically stretchable diaper closure elements that each comprise an inelastic and reinforced attachment region for securing a closure component and an adjacent elastic stretch region can be punched from a textile web. A plurality of pairs of elastic film strips of an elastically stretchable polymer are inserted between two cover layers of nonwoven with the film strips parallel and spaced laterally from one another. Between each pair of elastic film strips a strip of a reinforcement film is inserted that has a support layer and an outer layer of polyethylene on at least one side between the cover layers with each reinforcement-film strip overlapping each of the respective elastic film strips at a respective overlap region. The reinforcement-film strips are bonded to the elastic film strips in the overlap regions, and the nonwoven cover layers are bonded to the reinforcement film strips by ultrasonic or thermal welding.
