In this paper, some sufficient conditions for the local and global exponential stability of the discrete-time Hopfield neural networks with general activation functions are derived, which generalize those existing results. By means of Mmatrix theory and some inequality analysis techniques, the exponential convergence rate of the neural networks to the equilibrium is estimated, and for the local exponential stability, the basin of attraction of the stable equilibrium is also characterized. © 2004 Elsevier Ltd. All rights reserved.