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Abstract 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.