A brake system with anti-locking and/or traction slip control is disclosed including a brake pressure generator, an auxiliary pressure supply system having one or more bypass-regulated hydraulic pumps, and electrically controllable multi-way valves in the brake conduits. An auxiliary pressure supply system is connected either directly or through multi-way valves to the wheel brakes and, through separating valves, to the brake pressure generator. Inserted in bypass conduits which are connected in parallel to the hydraulic pumps, are additional multi-way valves which are normally closed in the rest position but which are reswitchable to an open position and by way of which the pressure in the auxiliary pressure supply system is controllable to modulate the brake pressure in the wheel brakes.