The invention relates to a braking and/or clamping device of a shaft that is mounted in an equipment housing or the device housing. Said device comprises a brake disc that is rotationally fixed on or to the shaft and a clamping ring that is mounted in the device housing. The brake disc has a friction region comprising two friction surfaces covering truncated cones. The device has at least one brake cone that is situated in the device housing and at least one brake cone that is located on an actuator. During the braking or clamping procedure, one brake cone is applied to the brake disc, whilst the other cone is applied to the clamping ring. The brake disc and the clamping ring make contact with one another between these application points. The invention permits the development of a braking and/or clamping device for rotating shafts that has a simple compact construction, producing strong clamping forces with short reaction times and that in addition is not prone to malfunction and requires no maintenance over its service life.