Disclosed is a steer-by-wire system and a control program therefor which are capable of preventing a steering handle from being turned excessively. According to the steer-by-wire system and the control program, when drive electric current to a steering actuator is restrained to restrict the steering of steerable road wheels, the steering reaction force to the steering handle is increased thereby to make the steering handle hard or unable to turn further. Thus, the steering handle can be prevented from being turned excessively. Further, when the steering actuator is heated beyond a predetermined temperature, such is judged as the overload on the steering actuator thereby to restrain the drive electric current to the steering actuator. Therefore, it can be obviated that the steering actuator is overheated to suffer failure.