In this paper, we are concerned with the dynamical behavior of the Leslie-Gower predator-prey system with time delay. First of all, we discuss the global stability for the Leslie-Gower predator-prey system without time delay. Next, we study the change of the global stability for the Leslie-Gower predator-prey system with time delay. Finally, we illustrate our results by some examples. 本篇論文主要分析Leslie-Gower捕食系統的整體穩定性。首先，利用Dulac’s Criterion+Poincare’Bendixon Theorem分析未具時滯參數之Leslie-Gower 捕食系統的整體穩定性。緊接著，利用Lyapunov Function 分析具時滯參數之Leslie-Gower捕食系統的整體穩定性。最後，用實例及電腦軌跡說明之。
