A container closure comprising cap means adapted for a turning on and off connection with holding means provided at the container opening to be closed, such as screw connection or bayonet connection, said cap means containing an outer cap means having elements for manupulation and an inner cap means having elements of said turning on and off connection and being mounted substantially within said outer cap means to be turned in and to be pushed into said outer cap means to a limited extent against the force of a spring, cooperating turning coupling elements, provided at said inner and outer cap means to be in engagement with each other when said inner cap means has been pushed axially into the outer cap means, cooperating supporting means at said inner and outer cap means comprising a supporting band extending round the circumference at the open end of said inner cap means to substantially improve supporting and guiding the said outer and inner cap means for their relative movements, and cooperating catch elements to secure the said inner cap means against its removal from the outer cap means, and an original package securing means adapted to be destroyed by first opening the container closure. Ratchetlike locking elements may be provided additionally at said inner and outer cap means independently from said turning coupling elements to lock said inner and outer cap means for turning said closure on said holding elements of the container and to form a freewheel connection in the direction of turning off said closure from the holding elements of the container.