A shiftable disk clutch or disk brake having two clutch parts which are rotatable relative to one another about a theoretical axis of rotation. One of the clutch parts has at least one rigid pressure disk which is connected with the clutch part so as to be fixed against movement and rigid. The other clutch part has at least two friction disks which are stiff in the circumferential direction and axially flexible in the manner of a diaphragm and are connected with this other clutch part so as to be fixed with respect to movement and rigid and are arranged on both sides of the pressure disk.