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In this paper, the existence and uniqueness of the equilibrium point and its global asymptotic stability are discussed for a general class of recurrent neural networks with time-varying delays and Lipschitz continuous activation functions. The neural network model considered includes the delayed Hopfield neural networks, bidirectional associative memory networks, and delayed cellular neural networks as its special cases. Several new sufficient conditions for ascertaining the existence, uniqueness, and global asymptotic stability of the equilibrium point of such recurrent neural networks are obtained by using the theory of topological degree and properties of nonsingular M-matrix, and constructing suitable Lyapunov functionals. The new criteria do not require the activation functions to be differentiable, bounded or monotone nondecreasing and the connection weight matrices to be symmetric. Some stability results from previous works are extended and improved. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.