An electric power steering system for a vehicle works to determine an assist command based on steering torque to produce assist torque through an electric motor for assisting in turning a steering wheel of the vehicle, also determines a tracking command for producing automatic steering torque which brings a value of a given physical quantity associated with steering of the vehicle into agreement a target value, and controls a response rate at which a value of a given physical quantity is brought into agreement with a target value in a feedback mode. A motor driver works to actuate an electric motor based on the sum of the assist command and the tracking command to output the torque for steering the system vehicle.