A　discrete　nonlinear　model　is　studied　and　sufficient　conditions　which　guarantee　the　permanence　of　the　model　are　obtained.　Assuming　that　the　coefficients　in　the　model　are　periodic,　the　existence　of　periodic　solutions　are　obtained.　Sufficient　conditions　are　obtained　to　ensure　the　global　stability　of　the　positive　periodic　solution　by　constructing　a　suitable　Lyapunov　function.　©　World　Scientific　Publishing　Company.