A　nonlinear　periodic　predator-prey　model　with　m-preys　and　(n　-　m)-predators　and　delays　is　studied,　which　can　be　seen　as　the　modification　of　the　traditional　Lotka-Volterra　prey-competition　model.　Two　sets　of　sufficient　conditions　which　guarantee　the　permanence　of　the　system　are　obtained.　One　set　is　delay　independent,　while　the　other　set　is　delay　dependent.　Our　results　supplement　those　obtained　by　Chen　et　al.　[F.D.　Chen,　X.D.　Xie,　J.L.　Shi,　Existence,　uniqueness　and　stability　of　positive　periodic　solution　for　a　nonlinear　prey-competition　model　with　delays,　Journal　of　Computational　and　Applied　Mathematics　194　(2)　(2006)　368-387].　©　2007　Elsevier　Inc.　All　rights　reserved.