Using a model calculation, desired changes in the yaw rate .DELTA..phi. and the transverse acceleration .DELTA.y are determined from a small change actually made in the steering angle and are compared to measured quantities .DELTA..phi..sub.F and .DELTA.y.sub.F determined on the vehicle. The deviations of the actual values of yaw rate and transverse acceleration from the calculated values are weighted using predetermined weighting factors for the relative importance of yaw rate and transverse acceleration and supplied with factors dependent on the individual wheel; finally, the values relating to the same wheel are added. They represent desired changes in the brake slip values and a controller finally converts these into brake slip value changes.