A steering system for the front and rear wheels of an automotive vehicle comprises a front wheel steering mechanism having an output shaft, a rear wheel steering mechanism having an input shaft coupled to the output shaft, an output member for steering the rear wheels, and a motion converting mechanism for converting rotation of the input shaft to movement of the output member, a vehicle speed sensor, and a control unit connected to the vehicle speed sensor for controlling operation of the motion converting mechanism dependent on the vehicle speed detected by the vehicle speed sensor. The motion converting mechanism comprises a shaft angularly movable by the input shaft, the shaft having an arm extending radially from one end thereof, a guide mounted on the output member and extending in a vertical direction transverse to an axis of the output member, a slide assembly disposed between and interconnecting the arm and the guide, and a drive device controlled by the control unit for moving the slide assembly along the guide. The drive device includes a gear mechanism connected with said slide assembly and a pair of motors coupled to the gear mechanism for driving the same, the pair of motors being driven in association with each other.