A　nonlinear　periodic　predator-prey　model　with　m-preys　and　(n-m)-predators　and　delays　is　proposed　in　this　paper,　which　can　be　seen　as　the　modification　of　the　traditional　Lotka-Volterra　prey-competition　model.　Sufficient　conditions　which　guarantee　the　existence　of　a　unique　globally　attractive　positive　periodic　solution　of　the　system　are　obtained.　(c)　2005　Elsevier　B.V.　All　rights　reserved.