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This article deals with the global asymptotic stability problem for a class of neural networks with time-varying discrete and distributed delays. The activation functions are assumed to be neither monotonic nor differentiable, and two types of time-varying discrete delays are considered: one is differentiable and has bounded derivatives, and the other is continuous and may vary very fast. By constructing an appropriate Lyapunov-Krasovskii functional and employing a tighter inequality, new stability criteria dependent on both the lower bound and upper bound of the time-varying time delays are established to guarantee asymptotic stability for the addressed neural networks. It is shown that the new criteria improve some results from previous studies. Two simulation examples are given to show the effectiveness and the reduced conservatism of the proposed criteria.