In　this　paper,　we　propose　a　discrete　multispecies　Lotka-Volterra　competition　predator-prey　systems.　For　general　non-autonomous　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　a　globally　stable　positive　periodic　solution　of　the　system　are　obtained.　(c)　2006　Elsevier　Inc.　All　rights　reserved.