A fall-arrest apparatus comprises a cable drum (2) and a friction brake including a rotatable brake disc (14) which is pressed against a stationary brake ring (15). In the event that the drum accelerates in the unwinding direction to a certain speed, pawls (19,20) carried by the drum (2) are centrifuged into driving engagement with the brake disc (14) to cause braking of the drum. The apparatus incorporates a fail-safe brake member (24) which is in screw-threaded engagement with a fixed part and is mechanically coupled to the rotatable brake disc (14) so that rotation of the brake disc (14) causes the fail-safe brake member to be screwed towards an operative position in which it causes progressive braking force to be applied between co-operating braking members (24,27,29).