Brake system for motor vehicles which, in a brake-by-wire operating mode, can be activated both by the vehicle driver and also independently of the vehicle driver, is preferably operated 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 hydraulic piston-cylinder arrangement having a hydraulic piston on which an actuating force (pedal force) is exerted when the brake system is actuated by the vehicle driver and which is guided displaceably in a housing along an actuation axis, b) a hydraulically actuable pedal travel simulator which is releasable and blockable by means of a simulator release valve, c) a travel detection device which detects the actuation travel of the piston, d) a pressure medium reservoir, e) an electrically controllable pressure source which delivers a brake system pressure, f) a pressure modulation unit having electrically controllable pressure regulating valves (6a-6d) for adjusting wheel-individual brake pressures which are derived from a brake system pressure, the brake system pressure being supplied via a brake system pressure line to the inlet connections of the pressure regulating valves (6a-6d) which deliver or transmit the brake system pressure in the unactivated state, g) dividing piston devices (5a-5d) which are associated with the motor vehicle wheel brakes (8, 9, 10, 11) and are subjected on a first dividing piston surface (41a-41d) to the pressure set or transmitted by the pressure regulating valves (6a-6d) and which transmit the pressure exerted by a second dividing piston surface (42a-42d) to the motor vehicle wheel brakes (8, 9, 10, 11), h) activating elements (17a-17d) for exerting the actuating force or for mechanically activating the dividing piston devices (5a-5d), which activating elements (17a-17d) can be brought into force-transmitting connection with the piston, and i) an electronic control and regulation unit, wherein j) the piston is guided directly in the housing. a) a brake pedal for actuating a hydraulic piston-cylinder arrangement having a hydraulic piston on which an actuating force (pedal force) is exerted when the brake system is actuated by the vehicle driver and which is guided displaceably in a housing along an actuation axis, b) a hydraulically actuable pedal travel simulator which is releasable and blockable by means of a simulator release valve, c) a travel detection device which detects the actuation travel of the piston, d) a pressure medium reservoir, e) an electrically controllable pressure source which delivers a brake system pressure, f) a pressure modulation unit having electrically controllable pressure regulating valves (6a-6d) for adjusting wheel-individual brake pressures which are derived from a brake system pressure, the brake system pressure being supplied via a brake system pressure line to the inlet connections of the pressure regulating valves (6a-6d) which deliver or transmit the brake system pressure in the unactivated state, g) dividing piston devices (5a-5d) which are associated with the motor vehicle wheel brakes (8, 9, 10, 11) and are subjected on a first dividing piston surface (41a-41d) to the pressure set or transmitted by the pressure regulating valves (6a-6d) and which transmit the pressure exerted by a second dividing piston surface (42a-42d) to the motor vehicle wheel brakes (8, 9, 10, 11), h) activating elements (17a-17d) for exerting the actuating force or for mechanically activating the dividing piston devices (5a-5d), which activating elements (17a-17d) can be brought into force-transmitting connection with the piston, and i) an electronic control and regulation unit, wherein j) the piston is guided directly in the housing.