The theoretical development of a direct adaptive tracking control architecture using neural networks is presented. Emphasis is placed on utilization of neural networks in a flight control architecture based on feedback linearization of the aircraft dynamics, Neural networks are used to represent the nonlinear inverse transformation needed for feedback linearization. Neural networks may be first trained offline using a nominal mathematical model, which provides an approximate inversion that can accommodate the total flight envelope, Neural networks capable of on-line learning are required to compensate for inversion error, which may arise from imperfect modeling, approximate inversion, or sudden changes in aircraft dynamics. A stable weights adjustment rule for the on-line neural network is derived. Under mild assumptions on the nonlinearities representing the inversion error, the adaptation algorithm ensures that all of the signals in the hoop are uniformly bounded and that the weights of the on-line neural network tend to constant values. Simulation results far an F-18 aircraft model are presented to illustrate the performance of the on-line neural network based adaptation algorithm.