A brake system for a motor vehicleincludes a first unit, a second unit, and a pressure medium reservoir which is under atmospheric pressure. The first unit includes a first electrically actuable pressure supply device having a hydraulic pressure chamber, wherein the first electrically actuable pressure supply device is hydraulically connected to a first and a second output pressure port of the first unit, and wherein the second unit includes a first input port, which is hydraulically connected to at least one first wheel port of the second unit, a second input port, which is hydraulically connected to at least one second wheel port of the second unit, a second electrically actuable pressure supply device, which is hydraulically connected to the at least one first and the at least one second wheel port, and at least one inlet valve per first and second wheel port.