A braking system for a vehicle is described, including a hydraulic service braking system and an electric service braking system having wheel brakes, to which braking pressure is applied when a brake pedal is operated. To maintain essentially constant vehicle braking behavior during a change in the braking-force distribution between the hydraulic and the electric service braking systems, it is proposed to provide a control unit, which is capable of varying the braking-force distribution and to equip the hydraulic service braking system with a braking pressure modulator that is controlled by the control unit and is able to effect a variable braking-force distribution as a function of the control by the control unit.