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This brief proposes an adaptive neural sliding mode control method for trajectory tracking of nonholonomic wheeled mobile robots with model uncertainties and external disturbances. The dynamic model with model uncertainties and the kinematic model represented by polar coordinates are considered to design a robust control system. Self recurrent wavelet neural networks (SRWNNs) are used for approximating arbitrary model uncertainties and external disturbances in dynamics of the mobile robot. From the Lyapunov stability theory, we derive online tuning algorithms for all weights of SRWNNs and prove that all signals of a closed-loop system are uniformly ultimately bounded. Finally, we perform computer simulations to demonstrate the robustness and performance of the proposed control system.