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We propose, from an adaptive control perspective, a neural controller for a class of unknown, minimum phase, feedback linearizable nonlinear system with known relative degree. The control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural-network structure. The resulting controller, however, moves the complex mechanics involved in a typical backstepping design from off-line to online. With appropriate choice of the network size and neural basis functions, the same controller can be trained online to control different nonlinear plants with the same relative degree, with semi-global stability as shown by the simple Lyapunov analysis. Meanwhile, the controller also preserves some of the performance properties of the standard backstepping controllers. Simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller.