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This paper performs a global stability analysis of a particular class of recurrent neural networks (RNN) with time-varying delay. Both Lipschitz continuous activation functions and monotone nondecreasing activation functions are considered. Globally delay-dependent robust stability criteria are derived in the form of linear matrix inequalities (LMI) through the use of Leibniz-Newton formula and relaxation matrices. Finally, two numerical examples are given to illustrate the effectiveness of the given criterion.