Two　asymptotically　cooperative　Lotka-Volterra　populations　in　the　two-patch-system　with　diffusion　were　considered　in　this　paper.　Each　population　could　diffuse　independently　and　discretely　between　its　intrapatch　and　interpatch.　By　means　of　constructing　a　suitable　Liapunov　function,　we　obtained　that　the　systems　had　a　unique　asymptotically　periodic　solution　which　was　globally　asymptotically　stable.　(c)　2006　Published　by　Elsevier　Inc.