Abstract: In this study, an adaptive output recurrent cerebellar model articulation controller (AORCMAC) is investigated for a nonlinear system. The proposed AORCMAC has superior capability to the conventional cerebellar model articulation controller in efficient learning mechanism and dynamic response. The dynamic gradient descent method is adopted to online adjust the AORCMAC parameters. Moreover, the analytical method based on a Lyapunov function is proposed to determine the learning-rates of AORCMAC so that the stability of the system can be guaranteed. Furthermore, the variable optimal learning-rates are derived to achieve the best convergence of tracking error. Finally, the effectiveness of the proposed control system is verified by the several simulation and experimental results. Those results show that the favorable performance can be obtained by using the proposed AORCMAC.