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The paper deals with the problem of model reference adaptive control of a class of uncertain nonlinear systems by output feedback based on neural networks. The uncertainty of the system can not be parameterized and its upper bound is unknown. In order to approximate the uncertainty via neural networks, a technique of global approximation of continuous functions is introduced. Based on the technique, a method of designing adaptive tracking controllers for the systems is presented, which guarantees that all signals in the closed loop system are bounded and the tracking error converges to a desired neighborhood of zero.