A method for operating a hydraulic motor vehicle brake system, in the event of a malfunction of the second functional unit includes the steps of generating a hydraulic pressure by means of the first hydraulic pressure generator and controlling at least one of the first valve assembly and the second valve assembly in such a way that a lower hydraulic pressure is established at the rear wheel brakes than at the front wheel brakes. The vehicle brake system includes a first functional unit, a second functional unit, and a control system. The first functional unit includes at least one first hydraulic pressure generator, a first valve assembly, and a second valve assembly, which is arranged between the first hydraulic pressure generator and the rear wheel brakes. The second functional unit includes at least one second, electric hydraulic pressure and a third valve assembly.