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To avoid unstable leing, a stable adaptive leing algorithm was proposed for discrete-time recurrent neural networks. Unlike the dynamic gradient methods, such as the backpropagation through time and the real time recurrent leing, the weights of the recurrent neural networks were updated online in terms of Lyapunov stability theory in the proposed leing algorithm, so the leing stability was guaranteed. With the inversion of the activation function of the recurrent neural networks, the proposed leing algorithm can be easily implemented for solving varying nonlinear adaptive leing problems and fast convergence of the adaptive leing process can be achieved. Simulation experiments in patt recognition show that only 5 iterations are needed for the storage of a 15X15 binary image patt and only 9 iterations are needed for the perfect realization of an analog vector by an equilibrium state with the proposed leing algorithm.