A wheel speed control apparatus for controlling a braking force and/or a driving force to be transmitted to wheels for maintaining the difference between the peripheral speed of each of the wheels and a vehicle running speed or an inferred value thereof at such position of the wheels at a value approximating the optimum value. The apparatus comprises a normal control for detecting and controlling the increase or incipient increase of the difference over the absolute value on the basis of a differential value of the difference and difference or the rotational speed of the wheels, and an integrating control for detecting and controling the continuation for a certain period of slightly excessive tendency of the absolute value of the difference, by comparing with a predetermined threshold value one of values which is smaller than the value with which, when the differential value is zero, the normal control would determines the excessive difference only with the absolute value.
