A bicycle hub brake wherein a rotating member (10) rotates with a bicycle wheel, and a brake actuating mechanism (5) causes a brake member (11) to apply a braking force to a braking surface. An intermediate member (14) is disposed between the brake actuating mechanism (5) and the rotating member (10) for moving relative to one of the brake actuating mechanism (5) or the rotating member (10) when a braking force less than a selected value is applied to the braking surface and for moving relative to the other one of the brake actuating mechanism (5) or rotating member (10) when a braking force greater than the selected value is applied to the braking surface.