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A recurrent wavelet-based cerebellar model articulation controller (RWCMAC) neural network used for solving the prediction and identification problem is proposed in this paper. The proposed RWCMAC has superior capability to the conventional cerebellar model articulation controller (CMAC) neural network in efficient learning mechanism, guaranteed system stability and dynamic response. The recurrent network is embedded in the RWCMAC by adding feedback connections in the mother wavelet association memory space so that the RWCMAC captures the dynamic response, where the feedback units act as memory elements. The dynamic gradient descent method is adopted to adjust RWCMAC parameters on-line. Moreover, the analytical method based on a Lyapunov function is proposed to determine the learning-rates of RWCMAC so that the variable optimal learning-rates are derived to achieve most rapid convergence of identifying error. Finally, the RWCMAC is applied in two computer simulations. Simulation results show that accurate identifying response and superior dynamic performance can be obtained because of the powerful on-line learning capability of the proposed RWCMAC.