Abstract: The dynamic behaviour of a class of generalized Hopfield neural networks with hysteresis is investigated. Relaxing the restriction that an interconnecting structure must be symmetrical in Hopfield neural networks, the stability of a class of the generalized Hopfield neural network models with hysteresis and asymmetric interconnecting structure is considered. The sufficient condition of the asymptotic stability of equilibrium point is given by way of constructing suitable Lyapunov functional and sectorial conditions. In the process of design and implementation of Hopfield neural networks, the condition is very applicable. The simulation results have proved further the effectiveness of the conclusion.