The adaptive control of dynamic systems with nonlinear parametrization is considered. An algorithm based on a neural network, similar to the TANN algorithm proposed in Annaswamy and Yu (1996), is suggested for adjusting the control parameters. The resulting adaptive controller is shown to lead to stability of the closed-loop system. How the neural network is trained off-line in order to lead to closed-loop stability is described in detail. The resulting improvement in performance using this neural controller over other methods proposed in the literature including extended Kalman filter, linear adaptive control, and other neural strategies is demonstrated through simulation studies.