In this paper, we investigate the global attractivity of Cohen-Grossberg neural network models with connection time delays for both discrete and distributed cases via the Lyapunov functional method. Without assuming the monotonicity and differentiability of activation functions and the symmetry of connection matrix, we establish three new sufficient conditions for the global exponential stability of a unique equilibrium for the delayed Cohen-Grossberg neural network no matter whether the connection time delay is of discrete type or distributed type. In particular, all the three new criteria are independent of time delays and do not include one another. To demonstrate the differences and features of the new stability criteria, several examples are discussed to compare the present results with the existing ones. (C) 2007 Elsevier Ltd. All rights reserved.