A brake system for a motor vehicle with four wheels has four electrically controlled wheel brake devices. Each of the wheel brake devices has a control part and an actuator, with which the various wheel brakes are activated independently of one another in response to actuations of the brake pedal by the driver. The brake system has two separate electrical control units, each for a respective two of the four wheel brake devices. Both of the separate control units receive control signals separately from a brake force simulator, and they each have their own energy supply circuit. An additional central control unit controls additional functions of the system (ABS, traction control, etc.) at each of the four wheel brake devices which serve safety or comfort purposes of the motor vehicle.