A device for steering the rear wheels of a vehicle having a first motor controlled at least with respect to the steering angle of the steering wheel (7), a gear change mechanism for changing gear ratios, a second motor for controlling the gear ratio by driving the gear change mechanism, a steering mechanism (14) for steering the rear wheels by transmitting a portion of the force equal to the product of the amount that the first motor is driven and the amount that the second motor is driven, a motor failure determination device for detecting motor failure when the amount that either of the first or second motors is driven is zero and the other of the motors is operated, and a control device for controlling both motors so that when motor failure is detected in one of the motors, the amount that the other motor is driven is brought to zero. The steering device may further have a sensor (29) for detecting the steering angle of the rear wheels, and a sensor failure detecting device which monitors the steering angle detected by the sensor, and detects a failure of the sensor when the steering angle of the rear wheel changes although the amount that one of the motors is driven is zero. Also disclosed is a process for steering the rear wheels of a vehicle.