Brake system for a motor vehicle with at least four hydraulically actuable wheel brakes (8a-8d), comprising • a first electrically controllable pressure source which is connected to a first brake circuit supply line such that it can be disconnected via a first cut-off valve, • a second electrically controllable pressure source which is connected to a second brake circuit supply line such that it can be disconnected via a second cut-off valve, • at least four electrically actual ball inlet valves (6a-6d) for setting wheel-individual brake pressures, each inlet valve being assigned to one of the wheel brakes, the first brake circuit supply line being connected to two of the inlet valves (6c, 6d), and the second brake circuit supply line being connected to the two other inlet valves (6a, 6b), • an electrically actuable outlet valve (7a-7d) per wheel brake (8a-8d) for discharging pressure medium from the wheel brake into a pressure medium storage reservoir which, in particular, is under atmospheric pressure, • an electrically actuable circuit cut-off apparatus, by way of which the first brake circuit supply line and the second brake circuit supply line are hydraulically disconnected when the circuit cut-off apparatus is in an unactuated state, and by way of which the first brake circuit supply line and the second brake circuit supply line are connected hydraulically to one another when the circuit cut-off apparatus is in an actuated state, • a first electronic apparatus, by means of which the first pressure source is actuated, and • a second electronic apparatus, by means of which the second pressure source is actuated, the second electronic apparatus being electrically independent of the first electronic apparatus, characterized in that the first cut-off valve is actuated by the second electronic apparatus, and the second cut-off valve is actuated by the first electronic apparatus. • a first electrically controllable pressure source which is connected to a first brake circuit supply line such that it can be disconnected via a first cut-off valve, • a second electrically controllable pressure source which is connected to a second brake circuit supply line such that it can be disconnected via a second cut-off valve, • at least four electrically actual ball inlet valves (6a-6d) for setting wheel-individual brake pressures, each inlet valve being assigned to one of the wheel brakes, the first brake circuit supply line being connected to two of the inlet valves (6c, 6d), and the second brake circuit supply line being connected to the two other inlet valves (6a, 6b), • an electrically actuable outlet valve (7a-7d) per wheel brake (8a-8d) for discharging pressure medium from the wheel brake into a pressure medium storage reservoir which, in particular, is under atmospheric pressure, • an electrically actuable circuit cut-off apparatus, by way of which the first brake circuit supply line and the second brake circuit supply line are hydraulically disconnected when the circuit cut-off apparatus is in an unactuated state, and by way of which the first brake circuit supply line and the second brake circuit supply line are connected hydraulically to one another when the circuit cut-off apparatus is in an actuated state, • a first electronic apparatus, by means of which the first pressure source is actuated, and • a second electronic apparatus, by means of which the second pressure source is actuated, the second electronic apparatus being electrically independent of the first electronic apparatus,