Proposed is a brake system for motor vehicles, which brake system, in a "brake by wire" operating mode, can be activated both by the vehicle driver and also independently of the vehicle driver, and which brake system is operated preferentially in the "brake by wire" operating mode and can be operated in a fall-back operating mode in which it can be activated only by the vehicle driver. The brake system has
inter alia a pedal force actuating element (2) which is connected to a brake pedal (1) and which is guided in a retaining piston (3) which, in a housing (20), delimits at least one retaining chamber (4). Also provided are dividing piston devices (5a-d) which interact with the retaining piston (3) and to which vehicle wheel brakes are connected. To attain a design of the brake system which is simple to realize, it is proposed according to the invention that the first dividing piston surface (9a-d) and the second dividing piston surface (10a-d) are formed on a first dividing piston portion (7a-d) and the first dividing piston surface (9a-d), together with a third dividing piston surface (11a-d) formed on a second dividing piston portion (8a-d), delimits an intermediate chamber (16a-d) which is connected to the electrohydraulic pressure generating device (14) via in each case one pressure modulation valve (6a-d) by means of which both a build-up of pressure in and also a discharge of pressure from the intermediate chamber is realized.