Two kinds of active control systems, using neural networks (NN), are presented for realizing optimal driving motion of four wheel steer (4WS) cars. The first system is based on the assumption that the car is simplified as a linear two wheel bycycle model, and that the friction force between tire and road surface is represented by Fiala's nonlinear model. The nonlinear relation between the slip angle of tire and the cornering force is expressed with NN. A model-following type control strategy is adopted in the first system, with both the feedforward and feedback gains for the control of the rear wheel steering angle adaptively determined with NN according to change of front wheel steering angle. The second system is based on the assumption that both the dynamical characteristics of the car and the tire friction force are nonlinear. The nonlinear dynamical characteristics of the car and the friction force are identified with NN, using the measured data of an actual car. The second control system is composed of only the NN model. It becomes evident by the simulation and the experiment using an actual car that driving performance of a car with the active control systems presented is far better than that of a car with the usual control system of fixed control gain.