An electrohydraulic brake system, comprising a brake master cylinder. A pressure generating device for actuating wheel brakes and an additional brake actuator may both be activated electronically. In a normal mode of operation, an open- and closed-loop control unit detects a braking demand based on the actuation of a brake pedal by the driver and activates the pressure generating device to build up braking torque at the wheel brakes. If the pressure generating device is not activated, the driver gains direct access to the wheel brakes and the control unit activates the additional brake actuator to build up braking torque. In the fallback mode, when a predetermined pedal travel threshold value is reached, the control loop activates the additional brake actuator to build up braking torque. In the event of a succession of brake pedal actuations by the driver, the pedal travel threshold value is increased at least once.