Abstract. In this paper, some sufficient conditions are obtained to guarantee that discrete time cellular neural networks (DTCNNs) can have some stable memory patterns. These conditions can be directly derived from the structure of the neural networks. Moreover, the method of how to estimate of the attracting domain of such stable memory patterns is also described in this paper. In addition, a new design algorithm for DTCNNs is developed based on stability theory (not based on the wellknown perceptron training algorithm), and the convergence of the design algorithm can be guaranteed by some stability theorems. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.