Brake system of a motor vehicle having front wheels (FL, FR) and rear wheels (RR, RL), comprising • a hydraulic service brake device having hydraulically actuatable first wheel brakes (8, 9) at the front wheels and hydraulically actuatable second wheel brakes (10, 11) at the rear wheels, an electrically actuatable, in particular normally open, inlet valve (6a-6d) for each hydraulically actuatable wheel brake (8, 9, 10, 11), a brake-pedal-actuatable master brake cylinder, which is connected to the first wheel brakes (8, 9) via an electrically actuatable, in particular normally open, first isolating valve, a simulation device, which is connected hydraulically to the master brake cylinder and provides a pleasant brake pedal feel for a vehicle driver in a "brake-by-wire" operating mode, an electrically actuatable pressure-providing device for actuating the first and second wheel brakes in the "brake-by-wire" operating mode, wherein the pressure-providing device is connected to the first and the second wheel brakes (8, 9, 10, 11), • a parking brake device having electric-motor-actuatable wheel brakes (60, 61) at the rear wheels (RR, RL), and • an electronic open-loop and closed-loop control unit, characterized in that in a hydraulic fall back operating mode of the brake system, in the case of a brake pedal actuation by a vehicle driver, exclusively the first wheel brakes (8, 9) are connected to the master brake cylinder and supplied with pressure by the vehicle driver by means of the master brake cylinder, while the rear wheels (RR, RL) are braked exclusively by means of the electric-motor-actuatable wheel brakes; to this end the master brake cylinder in the normal state of the hydraulic service brake device is connected only to the hydraulically actuatable first wheel brakes at the front wheels, or the master brake cylinder in the normal state of the hydraulic service brake device is connected to the hydraulically actuatable first wheel brakes and to the hydraulically actuatable second wheel brakes at the rear wheels, wherein the inlet valves of the hydraulic rear wheel brakes are closed so that exclusively the hydraulic front wheel brakes are connected to the master brake cylinder and supplied with pressure by the vehicle driver by means of the master brake cylinder. • a hydraulic service brake device having hydraulically actuatable first wheel brakes (8, 9) at the front wheels and hydraulically actuatable second wheel brakes (10, 11) at the rear wheels, an electrically actuatable, in particular normally open, inlet valve (6a-6d) for each hydraulically actuatable wheel brake (8, 9, 10, 11), a brake-pedal-actuatable master brake cylinder, which is connected to the first wheel brakes (8, 9) via an electrically actuatable, in particular normally open, first isolating valve, a simulation device, which is connected hydraulically to the master brake cylinder and provides a pleasant brake pedal feel for a vehicle driver in a "brake-by-wire" operating mode, an electrically actuatable pressure-providing device for actuating the first and second wheel brakes in the "brake-by-wire" operating mode, wherein the pressure-providing device is connected to the first and the second wheel brakes (8, 9, 10, 11), an electrically actuatable, in particular normally open, inlet valve (6a-6d) for each hydraulically actuatable wheel brake (8, 9, 10, 11), a brake-pedal-actuatable master brake cylinder, which is connected to the first wheel brakes (8, 9) via an electrically actuatable, in particular normally open, first isolating valve, a simulation device, which is connected hydraulically to the master brake cylinder and provides a pleasant brake pedal feel for a vehicle driver in a "brake-by-wire" operating mode, an electrically actuatable pressure-providing device for actuating the first and second wheel brakes in the "brake-by-wire" operating mode, wherein the pressure-providing device is connected to the first and the second wheel brakes (8, 9, 10, 11), • a parking brake device having electric-motor-actuatable wheel brakes (60, 61) at the rear wheels (RR, RL), and • an electronic open-loop and closed-loop control unit,