Abstract: A slip-controlled hydraulic brake system for all-wheel driven motor vehicles equipped with lockable differentials (2, 3) is provided with sensors (S.sub.1 -S.sub.4, 33-36) for measuring the rotational behavior of the wheels. Electronic circuits (44) are provided for logic combining and processing the sensor signals, and for generating braking pressure control signals by way of which the brake pressure in the individual wheel brakes (16-19) is variable in response to the rotational behavior of the wheels and to a reference variable. To compensate the increased moments of inertia as a result of the moments transmission, by way of the lockable differentials (2, 3) in this brake system the brake pressure in the rear-wheel brakes (18, 19), can be modulated at a lower control frequency as compared with the brake pressure in the front-wheel brakes (16, 17).