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The problems of asymptotic stability for a class of nonlinear singular systems with time-delay are investigated in this paper. A delay-dependent sufficient condition for asymptotic stability is obtained by using Lyapunov stability theorems. Based on the result, the criterion is extended to a class of functions with double variables in the nonlinear uncertainty, which satisfies Lipschitz condition. Finally, a numerical example is given to illustrate the effectiveness of the main results.