It is well known that the prototype patterns in associative memories can be represented by stable equilibrium points of cellular neural networks (CNNs).Therefore, the stability of equilibrium points of CNNs is critical in associative memories based on CNNs.In this paper, some criteria about the stability of CNNs are established.in fact, these criteria give some constraint conditions for the relationship of parameters of CNNs.Compared with the previous works, our results relax the conservatism of the relationship of parameters and extend the range of the values of parameters.Two design procedures on the parameters of CNNs are given to achieve associative memories under our criteria.Finally, an example is given to verify the theoretical results and design procedures.