A class of Cohen-Grossberg neural networks where the neuron activations are modeled by discontinuous functions was considered. A tool,the chain rule for computing the time derivative along the neural network solutions of a nondifferentiable Lyapunov function,is used which enables us to apply a Lyapunov-like approach to differential equations with discontinuous right-hand side. By means of the Lyapunov-like approach,a general result is proved on global exponential convergence toward a unique equilibrium poi...