Abstract: A brake system which can be employed both for brake slip control and for traction slip control, wherein the brake slip control is performed according to the return delivery principle, while an open-loop system is set up during traction slip control. In order to manage with the same pump (10) in both cases, a valve system composed of a first non-return valve (16) and a second non-return valve (17) is provided at the suction side of the pump. The opening pressure of the first non-return valve (16) is greater than that of the second non-return valve (17). Further, the initial pressure of a low-pressure accumulator (9) is in excess of the opening pressure of the first non-return valve (16). The first non-return valve (16) is operative during brake slip control, while the second non-return valve (17) is operative during traction slip control. Switch-over can be effected for instance by the master cylinder pressure via a control line (18).