Brake system of the brake-by-wire type for a motor vehicle, having a brake pressure signal transmitter which can be activated by means of a brake pedal and which can be connected to wheel brakes of the vehicle outside the brake-by-wire operating mode, having a pressure source which can be actuated by means of an electronic control unit and which can be connected to the wheel brakes of the vehicle in the brake-by-wire operating mode, having means for sensing a driver deceleration request, and having a pedal travel simulator which interacts with the brake pedal and which is formed by at least one spring element and one damping element, and a restoring force, which acts on the brake pedal, can be simulated outside the brake-by-wire operating mode, independently of the actuation of the pressure source, and having an electrohydraulic device which can be actuated by means of the electronic control unit and which permits activation of the pedal travel simulator outside the brake-by-wire operating mode and at least partial deactivation of the pedal travel simulator outside the brake-by-wire operating mode. According to the invention there is provision for the damping element (15) to be either arranged in a locationally fixed fashion and to interact with the electrohydraulic device (9) which is connected to the brake pedal (1) or to be connected to the brake pedal and to interact with the electrohydraulic device (9) which is arranged in a locationally fixed fashion.