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In this paper,the authors are conced with the stability of the mix-delayed CohenGrossberg neural networks with nonlinear impulse by the nonsmooth analysis.Some novel sufficient conditions are obtained for the existence and the globally asymptotic stability of the unique equilibrium point,which include the well-known results on some impulsive systems and non-impulsive systems as its particular cases.The authores also analyze the globally exponential stability of the equilibrium point.Two examples are exploited to illustrate the feasibility and effectiveness of our results.