A brake system includes a first functional unit having at least one first hydraulic pressure generator, which is designed to build up a hydraulic pressure at a wheel brake, and a first hydraulic fluid reservoir, from which the first hydraulic pressure generator can draw in hydraulic fluid. The brake system furthermore comprises a second functional unit having at least one second, electric hydraulic pressure generator, which is controllable in order to build up a hydraulic pressure at the wheel brake, a check valve and at least one second hydraulic fluid reservoir, having an outlet, via which the second, electric hydraulic pressure generator can draw in hydraulic fluid, and an inlet, relative to which the check valve is arranged upstream in such a way that it has a blocking effect toward the inlet in respect of a flow direction.