We present a state-feedback control of a two-link flexible-joint robot. We use three-layer neural networks to learn the unknown parts of the desired control laws. Therefore, the control algorithm does not require the mathematical model representing the robot. The neural networks' weights are adapted on-line. Therefore, the control system can adapt to changes during operation such as payload changes. We use a smooth variable structure controller to handle uncertainties from the neural network approximation, external disturbances, deadzone, and backlash. In our simulation, we obtain the actual plant model from experiments