A combined vehicle brake which has a hydraulically actuable service brake and an electromechanically actuable parking brake device, a hydraulic service pressure space being delimited in a brake housing by a brake piston which can be acted upon by hydraulic pressure medium in order to execute service braking operations, so that the brake piston can be actuated along a piston longitudinal axis in order to achieve a braking action, and the parking brake device acting on the brake piston by a gear, in that the gear converts the rotational movement of an electromechanical actuator into a translational movement and causes an actuation of the brake piston in order to execute parking braking operations and holds the said brake piston in the actuated position, the gear having a threaded spindle and a threaded nut which are in contact with one another via a plurality of rolling bodies.