In　this　paper,　we　consider　a　nonautonomous　discrete　Lotka-Volterra　system　of　two　species　with　the　effect　of　toxic　substances.　We　prove　that　one　of　the　components　will　be　driven　to　extinction　while　the　other　will　be　globally　attractive　with　any　positive　solution　of　a　discrete　logistic　equation　under　some　conditions.　For　periodic　case,　we　also　obtain　another　set　of　sufficient　conditions　which　guarantee　the　extinction　and　the　existence　of　a　globally　stable　periodic　solution.　It　is　shown　that　toxic　substances　play　an　important　role　in　the　extinction　of　species.　Copyright　©2008　Watam　Press.