Abstract: The invention relates to a brake system for a vehicle having at least one brake circuit which includes at least one wheel brake, one inlet valve, one outlet valve, and one return device. The return device has at least one first pump device and one second pump device, having respective inlet valves and outlet valves. The pump devices have a delivery cycle offset from each other. An additional valve is located in every supply line of every pump device for preventing negative pressure produced in an intake phase of one of the pump devices from being applied to an inlet valve of another pump device.