The existence, uniqueness, globally exponential stability and speed of exponential con-vergence for a class of cellular neural networks are investigated. The existence of a unique equilibrium is proved under very concise conditions, and theorems for estimating the global convergence speed approaching the equilibrium and criteria for its globally exponential stability are derived, Considering synapse time delay, by constructing appropriate Lyapunov functional, the existence of a unique equilib-rium and its global stability for the delayed network are also proved. The results, which do not require the cloning template to be symmetric, are easy to use in network design.