Controller is designed to control operation of a rear-wheel steering apparatus typically provided in a four-wheel steering vehicle, and is based on electronic circuitry. In the electronic circuitry, a target-steering-angle setting section sets a target steering angle of the rear wheels. Actual-steering-angle measurement section measures an actual steering angle of the rear wheels. On the basis of the target steering angle and actual steering angle, a steering-angle adjustment section generates a motor drive signal to control the rotation of the motor in such a manner that a difference or offset between the target steering angle and the actual steering angle becomes zero. On condition that the motor is in a predetermined driving state, a motor-deceleration-amount calculation section is activated to calculate an actual rotating speed of the motor on the basis of the actual steering angle of the rear wheels and compares the calculated actual rotating speed of the motor with a prestored reference rotation speed. The motor-deceleration-amount calculation section operates to calculate a motor-rotation deceleration amount when the compared result indicates that the calculated actual rotating speed is higher than the reference rotation speed.