In　this　paper,　we　consider　a　delayed　non-autonomous　n-species　Gilpin-Ayala　competitive　system,　which　is　more　general　and　more　realistic　then　classical　Lotka-Volterra　competition　model.　By　means　of　Ahmad　and　Lazer＇s　definitions　of　lower　and　upper　averages　of　a　function,　we　give　the　average　conditions　for　the　permanence　of　the　system.　It　is　shown　that　our　result　is　the　generalization　of　those　of　Zhao　et　al.　[J.D.　Zhao,　J.F.　Jiang,　A.C.　Lazer,　The　permanence　and　global　attractivity　in　a　nonautonomous　Lotka-Volterra　system,　Nonlinear　Analysis:　Real　World　Applications,　5　(4)　(2004),　265-276].　Our　results　also　supplement　the　results　of　Fan　and　Wang　[M.　Fan,　K.　Wang,　Global　periodic　solutions　of　a　generalized　n-species　Gilpin-Ayala　competition　model,　Computer　and　Mathematics　with　Applications,　40　(2000),　1141-1151].　(c)　2005　Elsevier　Inc.　All　rights　reserved.