A tamper-evident security device (which may form a child-resistant closure for a container) comprises a cap member (12) formed with at least one window (13), and an inner member (10) arranged for screw-threaded engagement with a container or other member and co-operable with the cap member (12) for rotation thereby: the inner member (10) carries at least one active element (11) arranged to displace outwardly and penetrate at least partially through the window (13) upon rotating the cap member (12) through a predetermined angle in the direction to loosen the inner member. In alternative arrangements, the cap member may be screw-threaded onto the inner member.