The operations of an electric power steering system and a wheel slip control system such as a traction control system or an anti-lock brake system are co-related so as not to undesirably affect one another, by the target assisting steering force for the electric power steering system being modified differently according to whether or not the wheel slip control system is in operation. In doing so, the target value of assisting steering force according to an increase of the steering torque of the steering wheel is increased by a degree increased along with increase of a time based differential of the steering torque of the steering wheel, or the degree of increasing the target value of assisting steering force according to an increase of the steering torque of the steering wheel is decreased along with increase of a time based differential of steering angle of the steering wheel.
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