Abstract: The invention relates to a vehicle hydraulic brake system with electrohydraulic brake boosting by a piston pump. In order to reduce pressure pulsations on an intake side of the multi-piston pump, the brake system embodies a multi-piston pump, for example, as a six-piston pump with stepped pistons that are driven with an alternating phase shift of 30° and 90° in relation to one another. The phase shift of the drive of the stepped pistons is selected so that the intake volume flows have a uniform phase shift, by which the total intake volume flow of the multi-piston pump has a reduced amplitude of the pressure pulsation, which reduces the repercussions on a master cylinder.