The stability of neural networks is a prerequisite for successful applications oftbe networks as eitber associative memories or optimization solvers. Because the integration and communication delays are ubiquitous, the stability of neural networks with delays has received extensive attention. However, the approach used in the previous investigation is mainly based on Liapunov's direct metbodi Since the construction of Liapunov traction is very skilful, tbere is little compatibility among the existing results, in tbis paper, we develop a new approach to stability analysis of Hopfield-type neural networks with time varying delays by defining two novel quantities of nonlinear traction similar to the matrix norm and the matrix measure, respectively. With the new approach, we present suffcient conditions of the stability, which are eitber the generalization of those existing or new. The developed approach may be also applied for any general system with time delays ratber than Hopfield-type neural networks.