PURPOSE: To suppress an influence of an error of a wheel speed at an ASR by depending upon a change of an engine rotational speed with a variable rising limit.

CONSTITUTION: A controller 5 generates a wheel speed signal filtered to obtain a brake slip, and a vehicle speed signal has a predetermined rising limit, that is, a maximum gradient of a wheel speed rise like, for example, 50 g. The wheel speed VABS left and VABS right of the drive wheel are also supplied to the controller 9 for the ARS through leads 7, 8. Further, the controller 5 obtains a reference speed signal from the wheel speed signal of the non-drive wheel, and the reference signal is supplied to a controller 9 through the lead 10 as a wheel speed for forming a slip in the case of the ASR. The speed signal is always generated in the vehicle during traveling. An engine tachometer 11 supplies an engine rotational speed Nmot.