A brake system for motor vehicles, which in a “brake by wire” mode, can be activated both by the vehicle driver and also independently of the vehicle driver, which is operated preferentially in the “brake by wire” operating mode and can be operated in a fall-back mode. A pedal force actuating element connected to a brake pedal is guided in a retaining piston forming a retaining chamber. Dividing piston devices interact with the retaining piston and connected to vehicle wheel brakes. The first dividing piston and the second dividing piston surface are formed on a first dividing piston portion and the first dividing piston surface, together with a third dividing piston surface formed on a second dividing piston portion form an intermediate chamber connected to electrohydraulic pressure generating device. A pressure modulation valve enables both a build-up of pressure in and also a discharge of pressure from the intermediate chamber.