Estimate of exponential convergence rate and exponential stability are studied for a class of neural networks which includes the Hopfield neural networks and the cellular neural networks. Both local and global exponential convergence is discussed. Theorems for estimate of exponential convergence rate are established and the bounds on the rate of convergence are given. The domains of attraction in the case of local exponential convergence are obtained. Simple conditions are presented for checking exponential stability of the neural networks.