Brake actuation unit for a brake-by-wire motor vehicle brake system having • a brake-pedal-actuable master brake cylinder having at least one master brake cylinder pressure space (17, 18) to which hydraulically actuable wheel brakes (8a-8d) of the motor vehicle can be connected, a pressure medium reservoir vessel which is assigned to the master brake cylinder and is under atmospheric pressure, • an electrically controllable pressure supply device which is formed by a hydraulic cylinder-piston arrangement whose piston can be actuated by an electric motor having a rotor and a stator, wherein the piston bounds a pressure space which is sealed with respect to the atmosphere by a main sealing element and which has a pressure medium connection for connecting to the wheel brakes, • a first group of electrically actuable valves (6a-6d, 7a-7d) for setting wheel-specific brake pressures, • a second group of electrically actuable valves (23a, 23b, 26a, 26b) for disconnecting or connecting the wheel brakes from or to the master brake cylinder or from or to the pressure supply device, and • an electronic open-loop and closed-loop control unit (12, 12') for activating the pressure supply device, the first group of valves and the second group of valves, characterized in that after a predefined actuation of the piston the pressure space is sealed by an additional sealing element, in that the electric motor has at least two drive units which can be operated independently of one another and each have at least one winding for driving the rotor of the electric motor, and in that the electronic open-loop and closed-loop control unit comprises a first microcontroller and a second microcontroller, wherein the first microcontroller is designed to activate, in particular only, one of the drive units of the electric motor, and the second microcontroller is designed to activate, in particular only, the other of the drive units of the electric motor, and wherein the first and second microcontrollers are designed to activate (207, 307) the second group of valves. • a brake-pedal-actuable master brake cylinder having at least one master brake cylinder pressure space (17, 18) to which hydraulically actuable wheel brakes (8a-8d) of the motor vehicle can be connected, a pressure medium reservoir vessel which is assigned to the master brake cylinder and is under atmospheric pressure, • an electrically controllable pressure supply device which is formed by a hydraulic cylinder-piston arrangement whose piston can be actuated by an electric motor having a rotor and a stator, wherein the piston bounds a pressure space which is sealed with respect to the atmosphere by a main sealing element and which has a pressure medium connection for connecting to the wheel brakes, • a first group of electrically actuable valves (6a-6d, 7a-7d) for setting wheel-specific brake pressures, • a second group of electrically actuable valves (23a, 23b, 26a, 26b) for disconnecting or connecting the wheel brakes from or to the master brake cylinder or from or to the pressure supply device, and • an electronic open-loop and closed-loop control unit (12, 12') for activating the pressure supply device, the first group of valves and the second group of valves,