Abstract: The ecological model of a class of the two microbe populations with second-order growth rate was studied. The methods of qualitative theory of ordinary differential equations were used in the four-dimension phase space. The qualitative property and stability of equilibrium points were analysed. The conditions under which the positive equilibrium point exists and becomes and O⁺ attractor are obtained. The problems on Hopf bifurcation are discussed in detail when small perturbation occurs.