Abstract: In this paper,the overall stability of some nonlinear non-forced networks with the disposed parallel characteristic is studied. The anther puts foward some applied criterions for the overall asymptotic stability and overall exponential stability,and the example of continous Hopfield neural networks is discussed for the application.The result of the paper is applicable to the nonlinear non-forced network with nonreciprocal resistor and local active resistor.

Key words: Nonlinear non-forced networks, Overall stability