An easy-opening closure for hermetic sealing of the open end of a packaging container includes an end member for being double-seamed to the open end of the container and having an interior ledge portion defining a large central opening and a composite lidding member of at least two polymer layers defining a predetermined peel strength at an interfacial plane for controlled delamination of the two layers. The composite lidding member covers the central opening and is bonded to the ledge portion to define a bond strength greater than the peel strength of the two polymer layers. The lidding member has a continuous ring-shaped notch cut into the bottom polymer layer adjacent the ledge portion and a discontinuous ring-shaped notch cut into the top polymer layer and spaced inwardly from the first notch to define a small unnotched portion between its ends and to define with the first notch a ring member therebetween which is connected at the unnotched portion to the central portion of the lidding member. With this construction, the force required to open the closure from the inside of the container is greater than the force required to open the closure from the outside of the container. The closure is circumferentially opened by upward pulling of the bonded overlapping portion of the composite lidding member to cause delamination and peeling of the top polymer layer from the bottom polymer layer bonded to the end member in an area between the first notch and an outside circumference of the lidding member and removal of the ring member between the first and second notches.