The self-opener closure comprises a spout (2) having a projecting lower rim (9) which is to be molded or glued to a composite packaging, an associated rotary cap (1) as well as a self-opener sleeve (3) arranged within the spout (2). This self-opener sleeve (3) can be made to rotate by the rotary cap (1). The inner side of the spout (2) is provided with four guide webs having varying inclines arranged over its inner circumference. These interact with specially formed guide ribs at the outer wall of the self-opener sleeve (3), which brings about that the self-opener sleeve (3), when continuously rotated in the inside of the spout (2), and by being guided at these guide ribs, describes an uneven downwardly directed movement, which superposes its rotational movement. Thus, the self-opener sleeve (3) first pierces the paper or cardboard laminate with the tip (24) of its lancing mandrel in a steep, screwline downwardly directed movement, and thereafter completes a horizontal rotational movement about 340.degree., whilst it cuts a circular disk out of the laminate with its sharp cutting edge, and thereafter pivots this downwards and retains it in this position.