Summary: The convergence and existence of periodic solutions for neural networks are known as the basis of various applications. In this paper, the convergence and existence of periodic solutions for a class of discrete-time models of two-cell cellular neural networks with symmetric template are investigated. By using the Lyapunov direct method and LaSalle’s invariance principle, some new results are obtained about the stability, asymptotic stability, the existence and attractivity of 2-periodic solutions.