Method for operating a brake system of a motor vehicle, - wherein the brake system has a first hydraulic circuit, a second hydraulic circuit and a master brake cylinder, - wherein the first hydraulic circuit has at least a first hydraulic pump, which is driven by an electric motor, and a first switching valve, and the master brake cylinder is connected via the first switching valve to a first suction port of the first hydraulic pump, - wherein the first hydraulic circuit further has at least a first low-pressure accumulator and a first non-return valve, wherein the first low-pressure accumulator is connected via the first non-return valve to the first suction port of the first hydraulic pump, with the result that a throughflow direction of the first non-return valve is directed towards the first suction port, - wherein the second hydraulic circuit has at least a second hydraulic pump, which is driven by an electric motor, and a second switching valve, and the master brake cylinder is connected via the second switching valve to a second suction port of the second hydraulic pump, - wherein the second hydraulic circuit further has at least a second low-pressure accumulator and a second non-return valve, wherein the second low-pressure accumulator is connected via the second non-return valve to the second suction port of the second hydraulic pump, with the result that a throughflow direction of the second non-return valve is directed towards the second suction port, - wherein, during continuous running of the first hydraulic pump and the second hydraulic pump, the first switching valve and the second switching valve are opened and closed in an alternating manner to one another. - wherein the brake system has a first hydraulic circuit, a second hydraulic circuit and a master brake cylinder, - wherein the first hydraulic circuit has at least a first hydraulic pump, which is driven by an electric motor, and a first switching valve, and the master brake cylinder is connected via the first switching valve to a first suction port of the first hydraulic pump, - wherein the first hydraulic circuit further has at least a first low-pressure accumulator and a first non-return valve, wherein the first low-pressure accumulator is connected via the first non-return valve to the first suction port of the first hydraulic pump, with the result that a throughflow direction of the first non-return valve is directed towards the first suction port, - wherein the second hydraulic circuit has at least a second hydraulic pump, which is driven by an electric motor, and a second switching valve, and the master brake cylinder is connected via the second switching valve to a second suction port of the second hydraulic pump, - wherein the second hydraulic circuit further has at least a second low-pressure accumulator and a second non-return valve, wherein the second low-pressure accumulator is connected via the second non-return valve to the second suction port of the second hydraulic pump, with the result that a throughflow direction of the second non-return valve is directed towards the second suction port, - wherein, during continuous running of the first hydraulic pump and the second hydraulic pump, the first switching valve and the second switching valve are opened and closed in an alternating manner to one another.