A “brake-by wire” brake system for motor vehicles, with a brake master cylinder which can be actuated by a brake pedal and has a housing and a piston, which is arranged displaceably in the housing and, together with the housing, delimits a pressure space. The piston of the brake master cylinder is designed as a stepped piston with at least two hydraulic active surfaces A1, A2 of differing size, wherein a first, small active surface A1 is assigned to the pressure space, and a second, large active surface A2 is assigned to a filling space, and, after a closing travel has been overcome, the second, large hydraulic active surface A2 is effective and the active surface A2, A1 are switched over in dependence on a hydraulic pressure in the pressure space and on the pedal force, respectively.