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In this paper, the Cohen-Grossberg neural network models with variable coefficients and time-varying delays are considered. By constructing an appropriate Lyapunov functional, some global exponential stability criteria for this type of Cohen-Grossberg neural network are presented. These criteria are applicable for other neural network models, such as cellular neural networks. Our results are less conservative and restrictive than previously known results and can be easily verified. And the result has considered signs of the connecting weights. Some comparisons and an example are given to demonstrate the main results.