Abstract: An adjustment device for a brake actuator including a spindle (20) is arranged between an hydraulically movable piston (12) and a mechanically movable tappet (18). The spindle (20) is formed at its outside with left- and right-hand threads (26) and (28), respectively, on which a collet (22) and an adjusting nut (24), respectively, are threaded in non-self-locking manner or, in other words, reversibly. The collet (22) and the adjusting nut (24) form a conical coupling (25) which, when engaged or closed prevents rotation of the structural members so that the adjustment device acts as a rigid member between the tappet (18) and the piston (12).