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 preferably operated in the brake-by-wire operating mode and can be operated in at least one fallback operating mode, comprising • a brake master cylinder having a housing and two pistons (15, 16) which delimit in the housing two pressure chambers (17, 18) to each of which a respective brake circuit (I, II) having wheel brakes (8, 9, 10, 11) is connected, • a brake pedal coupled to the brake master cylinder for actuating the brake master cylinder, • an electrically actuable, currentlessly open inlet valve (6a-6d) and an electrically actuable, currentlessly closed outlet valve (7a-7d) for each wheel brake for setting wheel-individual brake pressures, • an electrically actuable, in particular currentlessly open, isolation valve (23a, 23b) for each brake circuit (I, II) for isolating the pressure chamber (17, 18) from the inlet connections of the inlet valves of the wheel brakes of the respective brake circuit, • a first electrically controllable pressure supply unit which is formed, in particular, by a cylinder-piston arrangement the piston of which is actuable by an electromechanical actuator, • an electrically actuable, in particular currentlessly closed, sequence valve (26a, 26b) for each brake circuit (I, II) for hydraulically connecting the first pressure supply unit to the inlet connections of the inlet valves of the wheel brakes of the brake circuit, • a simulation device which communicates to the vehicle driver an agreeable brake pedal feel in the brake-by-wire operating mode, and • a first electronic control and regulation unit for activating the first pressure supply unit, and in particular the isolation valves (23a, 23b) and the sequence valves (26a, 26b), characterized in that the simulation device is hydraulically connectable by means of an electrically actuable simulator release valve, in particular activated by the first electronic control and regulation unit, or mechanically actuable simulator release valve to at least one pressure chamber of the brake master cylinder, and in that a second electrically controllable pressure supply unit (49, 149) having at least one intake port and one pressure port is provided, whereof the intake port is connected to the outlet connection of one of the isolation valves (23a, 23b) and the pressure port is connected to the inlet connections of the associated inlet valves, the second pressure supply unit (49, 149) being able to draw pressure medium from the pressure chamber in an unenergized state of the isolation valves and of the inlet and outlet valves, and wherein the second pressure supply unit includes at least two hydraulic pumps (42, 42c) driven by an electric motor, the intake ports of the first and the second pump each being connected to one of the isolation valves (23a, 23b) and the pressure ports of the first and second pump being connected to the inlet connections of the associated inlet valves. • a brake master cylinder having a housing and two pistons (15, 16) which delimit in the housing two pressure chambers (17, 18) to each of which a respective brake circuit (I, II) having wheel brakes (8, 9, 10, 11) is connected, • a brake pedal coupled to the brake master cylinder for actuating the brake master cylinder, • an electrically actuable, currentlessly open inlet valve (6a-6d) and an electrically actuable, currentlessly closed outlet valve (7a-7d) for each wheel brake for setting wheel-individual brake pressures, • an electrically actuable, in particular currentlessly open, isolation valve (23a, 23b) for each brake circuit (I, II) for isolating the pressure chamber (17, 18) from the inlet connections of the inlet valves of the wheel brakes of the respective brake circuit, • a first electrically controllable pressure supply unit which is formed, in particular, by a cylinder-piston arrangement the piston of which is actuable by an electromechanical actuator, • an electrically actuable, in particular currentlessly closed, sequence valve (26a, 26b) for each brake circuit (I, II) for hydraulically connecting the first pressure supply unit to the inlet connections of the inlet valves of the wheel brakes of the brake circuit, • a simulation device which communicates to the vehicle driver an agreeable brake pedal feel in the brake-by-wire operating mode, and • a first electronic control and regulation unit for activating the first pressure supply unit, and in particular the isolation valves (23a, 23b) and the sequence valves (26a, 26b),