In　this　paper,　we　propose　a　discrete　Gilpin-Ayala　competition　model　and　a　discrete　Gilpin-Ayala　type　multispecies　competition-predator　model.　For　general　nonautonomous　case,　sufficient　conditions　which　ensure　the　permanence　and　the　global　stability　of　the　system　are　obtained;　For　periodic　case,　sufficient　conditions　which　ensure　the　existence　of　an　unique　globally　stable　positive　periodic　solution　of　the　system　are　obtained.　An　example　together　with　its　numeric　simulations　shows　the　feasibility　of　the　main　results.　©　2007　Elsevier　Ltd.　All　rights　reserved.