A motor vehicle “brake-by-wire” system having an actuating unit, including a brake master cylinder, actuatable by a brake pedal, has a housing and a piston, arranged displaceably in the housing and, with the housing, delimits a pressure space. The brake master cylinder piston is a stepped piston with two differing size hydraulic active surfaces; a first, small active surface assigned to the pressure space, and a second, large active surface assigned to a filling space. In the “brake-by-wire” operating mode, the filling space is connected to the travel simulator via a pressure medium line such that, in the “brake-by-wire” operating mode, the first small active surface is effective, and, in the recoil plane after a closing travel has been overcome, the second, large hydraulic active surface is effective and the active surfaces are switched over depending on a hydraulic pressure in the pressure space and on the pedal force, respectively.