A brake system of the brake-by-wire (BBW) type for a vehicle having a brake pressure signal generator which can be activated by a brake pedal and can be connected to wheel brakes outside the BBW operating mode, having a pressure source which can be actuated by an electronic control unit and can be connected to the brakes of the vehicle in the BBW operating mode, having provisions for sensing a driver's deceleration request and having a pedal travel simulator which interacts with the brake pedal. A restoring force acting on the brake pedal can be simulated in the BBW operating mode independently of the actuating of the pressure source, and having a device which can be actuated by the electronic control unit and which permits activation of the pedal travel simulator in the BBW operating mode and deactivation of the pedal travel simulator outside the BBW operating mode.