A steering system for a vehicle has a secondary wheel steering mechanism which steers the front wheels or rear wheels independently of the steering wheel. A main control system calculates the control variable on the basis of the difference between the actual yawing angle and the desired yawing angle which controls the secondary wheel steering mechanism with the control variable in such a way that the actual yawing angle converges with the desired yawing angle. A neural network control system has a neural network which has learnt control variables for the wheel steering angle as a function of a state variable of the vehicle. The control of the wheels is switched over from control by the main control system to control by the neural network control system when it is determined that the operating state of the vehicle is outside the range within which the stability of the vehicle is ensured by the wheel steering control by the main control system.
