An apparatus for determining a failure of wheel speed sensors, which is capable of properly determining whether or not a wheel speed detection
system including the wheel speed sensors has failed, if at least a wheel speed detected by the wheel speed sensors indicates a stopped state of a corresponding wheel. An engine rotational speed is detected, and an input-output rotational speed ratio of a
torque converter of an
automatic transmission mounted in the vehicle is calculated. A shift range of the
automatic transmission is detected. Whether or not the vehicle is traveling is determined based on the engine rotational speed and the input-output rotational speed ratio when the
automatic transmission is in a traveling range. It is determined that the wheel speed detection
system including the wheel speed sensors has failed, if it is determined that the vehicle is traveling, and at the same time, at least one of wheel speed sensors indicates a stopped state of a corresponding one of the wheels.