Abstract: A brake system includes a hydraulic actuating unit, which can be actuated by way of a brake pedal, a travel simulator interacting with the hydraulic actuating unit, a pressure medium reservoir under atmospheric pressure assigned to the hydraulic actuating unit, a first electrically controllable pressure supply device, a second electrically controllable pressure supply device, an electronic control unit and an electronically controllable pressure modulation device for setting wheel-specific brake pressures. The brake system preferably operates in a “brake-by-wire” mode but can also operate in a fallback mode. The second electrically controllable pressure supply device can provide boost volume during braking in a fallback mode.