In　this　paper,　we　consider　a　general　nonautonomous　n-species　Gilpin-Ayala　competitive　system,　which　is　more　general　and　more　realistic　than　classical　Lotka-Volterra　competition　model.　By　means　of　Ahmad　and　Lazer＇s　definitions　of　lower　and　upper　averages　of　a　function,　we　first　give　the　average　conditions　for　the　permanence　and　global　attractivity　of　the　system.　Next,　for　each　r　{less-than　or　slanted　equal　to}　n　the　average　conditions　on　the　coefficients　are　provided　to　guarantee　that　r　of　the　species　in　the　system　are　permanent　while　the　remaining　n　-　r　species　are　driven　to　extinction.　Examples　show　the　feasibility　of　the　main　results.　©　2005　Elsevier　Ltd.　All　rights　reserved.