A brake system for motor vehicles may have a main brake cylinder with a floating piston arranged therein, which hermetically seals first and second pressure chambers from one another. The first pressure chamber may be hydraulically connected to a first brake circuit, and the second pressure chamber may be hydraulically connected to a second brake circuit. The brake system may further include a pressure means reservoir under atmospheric pressure, wheel brakes, an electrically controllable pressure supply device for pressure build-up and pressure reduction in the wheel brakes, a valve block with a currentless open inlet valve/switching valve for each wheel brake and with at least one outlet valve, wherein each wheel brake can be hydraulically connected via the switching valve associated with it to a pressure chamber of the main brake cylinder.