A brake system operates on the back-flow principle during brake slip control and is furnished with a self-priming pump (9) to achieve, during traction slip control, a rapid response of the wheel brakes without requiring the use of a high-pressure accumulator. This is achieved by a low-pressure accumulator (6) of a special design which includes an intake channel (7) to the intake side of the pump (9) for brake slip control and a separate intake channel (8) to the intake side of the pump (9) for traction-slip control. During brake slip control, only a partial discharge of the low-pressure accumulator (6) up to a defined remaining standby volume, through the brake slip control intake channel (7), is enabled because a valve (24, 25) controlled by the piston stroke will then close. Upon commencement of a traction slip control action, a valve in the traction slip control intake channel (8) is opened electromagnetically. Thus, the standby volume, at a slight static pressure, is made available to the intake side of the pump (9), thereby eliminating extended intake distances.