A braking and/or clamping device for a shaft guided in relation to a basic body, includes an actuating assembly (10) and a shaft-coupling assembly (80). The actuating assembly comprises a split housing (11) which has two bending plates (15, 16) which can bulge elastically in certain regions. The bending plates each have gripper jaws (23, 24) with frictional surfaces (31, 32). A sealed pressure chamber (37), which can be filled with a pressure medium, is situated between the bending plates. Parts of a shaft-coupling assembly project between the clamping zones, said parts establishing and establish the linking to the braked or clamped shaft. When the pressure in the pressure chamber is relieved, the frictional surfaces of the actuating assembly can be applied to the frictional surfaces of the shaft-coupling assembly, thereby providing the braking and/or clamping force.