Abstract: An analysis is made of the existence, uniqueness and globally asymptotical stability of the equilibrium point of Hopfield neural networks. Without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence and uniqueness of the equilibrium are obtained. Using M-matrix theory, Liapunov function is constructed and employed to establish sufficient conditions for global asymptotic stability. These results are applicable to symmetric or nonsymmetric interconnection matrices, and to continuous non-monotonic neuron activation function