Tamper-evident closure for a container having an opening with a thread, the closure comprising: - an outer cap with a first sidewall and a first top wall, the first top wall comprising a tamper-evident member connected to a surrounding region by a frangible structure; - an inner cap with a second sidewall and a second top wall, the inner cap comprising a cap thread configured to cooperate with the container thread, the inner cap being coaxially nested in the outer cap with possibility of relative axial movement so that the first and second top walls (23, 43) can be displaced relative to each other in the direction of a main axis (X 1) of the closure; - at least one protruding element arranged between the first top wall and the second top wall while facing the tamper-evident member; - a first engagement mechanism (52, 54a; 62, 64a) between the outer cap and the inner cap, configured to drive the outer cap and the inner cap in unison in a direction of screwing (R 1) the cap thread onto the container thread, upon application on the outer cap of a rotational torque in the direction of screwing (R 1), to mount the closure on the container without breaking the frangible structure; - a second engagement mechanism (72, 74; 62, 64b) between the outer cap and the inner cap, configured to drive the outer cap and the inner cap in unison in a direction of unscrewing (R 2) the cap thread relative to the container thread, upon application on the outer cap of a rotational torque in the direction of unscrewing (R 2) at the same time as an axial force in the direction of the main axis (X 1), to remove the closure from the container; wherein the closure further comprises a third engagement mechanism (82, 84; 92, 94) between the outer cap and the inner cap, configured to break the frangible structure upon relative rotational movement of the outer and inner caps when the outer cap is rotated in the direction of unscrewing (R 2), regardless of an axial force applied on the outer cap in the direction of the main axis (X 1), - an outer cap with a first sidewall and a first top wall, the first top wall comprising a tamper-evident member connected to a surrounding region by a frangible structure; - an inner cap with a second sidewall and a second top wall, the inner cap comprising a cap thread configured to cooperate with the container thread, the inner cap being coaxially nested in the outer cap with possibility of relative axial movement so that the first and second top walls (23, 43) can be displaced relative to each other in the direction of a main axis (X 1) of the closure; - at least one protruding element arranged between the first top wall and the second top wall while facing the tamper-evident member; - a first engagement mechanism (52, 54a; 62, 64a) between the outer cap and the inner cap, configured to drive the outer cap and the inner cap in unison in a direction of screwing (R 1) the cap thread onto the container thread, upon application on the outer cap of a rotational torque in the direction of screwing (R 1), to mount the closure on the container without breaking the frangible structure; - a second engagement mechanism (72, 74; 62, 64b) between the outer cap and the inner cap, configured to drive the outer cap and the inner cap in unison in a direction of unscrewing (R 2) the cap thread relative to the container thread, upon application on the outer cap of a rotational torque in the direction of unscrewing (R 2) at the same time as an axial force in the direction of the main axis (X 1), to remove the closure from the container;