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A robust adaptive neural network control scheme is proposed for a class of strict-feedback nonlinear systems with unknown control directions and unmodeled dynamics. The proposed design method expands the class of nonlinear systems for which robust adaptive control approaches have been studied. A priori knowledge of the signs of the control directions is not required. It is proved that under the proposed control law, all the closed-loop signals are uniformly ultimately bounded and the output asymptotically converges to zero. Simulation study is provided to verify the theoretical results.