With Poincare’s inequality and auxiliary function applied in a class of retarded cel-lular neural networks with reaction-diffusion, the conditions of the systems’ W1,2(Ω)-exponential and X1,2(Ω)-asmptotic stability are obtained. The stability con-ditions containing diffusion term are different from those obtained in the previous papers in their exponential stability conditions. One example is given to illustrate the feasibility of this method in the end. With Poincare’s inequality and auxiliary function applied in a class of retarded cel-lular neural networks with reaction-diffusion, the conditions of the systems’ W1,2 (Ω) -exponential and X1,2 (Ω) -asmptotic stability are obtained. stability con-ditions containing diffusion term are different from those obtained in those obtained in the previous papers in their exponential stability conditions. One example is given to illustrate the feasibility of this method in the end.