A braking system having a master cylinder to which wheel brake circuits (I, II) can be connected, a first piston coupled to a brake pedal, a second piston by means of which the master cylinder is actuated, a third piston actuated by the first piston and connected in a force transmitting fashion to the second piston, a simulation device which gives the driver of the vehicle a pedal sensation, an intermediate space between the second piston and third piston, a pressure generating device which controls the pressure in the intermediate space, a pressure medium reservoir vessel which is under atmospheric pressure and which can be connected hydraulically to the intermediate space, and means for electrically controlling the pressure in the intermediate space.