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In this paper, the complete stability of cellular neural networks with time-varying delays is analyzed using the induction method and the contraction mapping principle. Delay-dependent and delay-independent conditions are obtained for locally stable equilibrium points to be located anywhere, which differ from the existing results on complete stability where the existence of equilibrium points in the saturation region is necessary for complete stability and locally stable equilibrium points can be in the saturation region only. In addition, some existing stability results in the literature are special cases of a new result herein. Simulation results are also discussed by use of two illustrative examples.