In　this　paper,　a　May　cooperative　system　with　strong　and　weak　cooperative　partners　is　proposed.　First,　by　using　differential　inequality　theory,　we　obtain　the　permanence　and　non-permanence　of　the　system.　Second,　we　discuss　the　existence　of　the　positive　equilibrium　point　and　boundary　equilibrium　point,　after　that,　by　constructing　suitable　Lyapunov　functions,　it　is　shown　that　the　equilibrium　points　are　globally　asymptotically　stable　in　the　positive　octant.　Finally,　examples　together　with　their　numerical　simulations　show　the　feasibility　of　the　main　results.　©　2018,　The　Author(s).