The local stability analysis of a neural network is essential in evaluating the performance of this network when it acts as associative memories. This paper addresses the local stability of the Cohen-Grossberg neural networks (CGNNs). A sufficient condition for the local exponential stability of an equilibrium point is presented, and the size of the attractive basin of a locally exponentially stable equilibrium is estimated. The proposed condition and estimate are easily checkable and applicable, because they are phrased only in terms of the network parameters, the nonlinearities of the neurons, and the relevant equilibrium point. To our knowledge, this is the first time that such an estimate for CGNNs has been presented. The utility of our results is illustrated via a numerical example. © 2008 Elsevier Ltd. All rights reserved.