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This paper studies the global convergence properties of continuous-time neural networks with multiple time delays. By employing suitable and more general Lyapunov functionals, we derive a new delay independent sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point. The results are applicable to all continuous non-monotonic neuron activation functions and do not require the interconnection matrices to be symmetric. The obtained results can be easily verified as they can be expressed in terms of the network parameters only. Some numerical examples are also given to compare our results with previous stability results derived in the literature.