Brake system for motor vehicles which, in a brake-by-wire operating mode, can be activated both by the vehicle driver and independently of the vehicle driver, is operated preferably in the brake-by-wire operating mode and can be operated in at least one fall-back operating mode in which only operation by the vehicle driver is possible, comprising: a) a brake pedal for actuating a pedal force transmitting element on which an actuating force is exerted when the brake system is actuated by the vehicle driver, which pedal force transmitting element is guided displaceably along an actuation axis in a hydraulic retaining piston which delimits a hydraulic retaining chamber in a housing, b) a travel detecting device which detects the actuation travel of the pedal force transmitting element, c) a travel simulator (13; 21, 22) which in the brake-by-wire operating mode communicates the usual brake pedal feel to the vehicle driver, which is in force-transmitting communication with the pedal force transmitting element and the effect of which can be switched off in the fall-back operating mode, d) an electrohydraulic pressure generating device which delivers a brake system pressure, e) electrically controllable pressure modulation valves (6a-d) for setting wheel-individual brake pressures which are derived from the brake system pressure, the pressure modulation valves (6a-d) delivering or transmitting the brake system pressure in the unactivated state, f) dividing piston devices (5a-d; 7a-d, 8a-d) which are subjected on a first dividing piston surface (9a-d) to the pressure set or transmitted by the pressure modulation valves (6a-d), and on a second dividing piston surface (10a-d) build up a pressure which is transmitted via hydraulic connections to the wheel brakes, g) activating elements (17a-d) for mechanically activating the dividing piston devices (5a-d; 8a-d), and h) an electronic control and regulation unit, characterized in 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) delimits with a third dividing piston surface (11a-d) formed on a second dividing piston portion (8a-d) an intermediate chamber (16a-d) which is connected to the electrohydraulic pressure generating device via one pressure modulation valve (6a-d) in each case, by means of which pressure modulation valve (6a-d) both a pressure build-up and a pressure reduction are effected in the intermediate chamber (16a-d). a) a brake pedal for actuating a pedal force transmitting element on which an actuating force is exerted when the brake system is actuated by the vehicle driver, which pedal force transmitting element is guided displaceably along an actuation axis in a hydraulic retaining piston which delimits a hydraulic retaining chamber in a housing, b) a travel detecting device which detects the actuation travel of the pedal force transmitting element, c) a travel simulator (13; 21, 22) which in the brake-by-wire operating mode communicates the usual brake pedal feel to the vehicle driver, which is in force-transmitting communication with the pedal force transmitting element and the effect of which can be switched off in the fall-back operating mode, d) an electrohydraulic pressure generating device which delivers a brake system pressure, e) electrically controllable pressure modulation valves (6a-d) for setting wheel-individual brake pressures which are derived from the brake system pressure, the pressure modulation valves (6a-d) delivering or transmitting the brake system pressure in the unactivated state, f) dividing piston devices (5a-d; 7a-d, 8a-d) which are subjected on a first dividing piston surface (9a-d) to the pressure set or transmitted by the pressure modulation valves (6a-d), and on a second dividing piston surface (10a-d) build up a pressure which is transmitted via hydraulic connections to the wheel brakes, g) activating elements (17a-d) for mechanically activating the dividing piston devices (5a-d; 8a-d), and h) an electronic control and regulation unit,