This paper is concerned with an analysis of sufficient conditions of hydrodynamic stability of convective disperse flows. The applicability of this kind of researches is raised with an obvious need to consider the influence of nonhomogeneous effects or flow complications on heat-mass transfer characteristics. In particular, flows of two-phase systems are common in nature and technical applications. The sufficient conditions of disperse flow stability are analytically defined. The qualitative theoretical explanation of an effect dealing with sufficient flow stabilization at certain values of dispersion degree is presented. This effect was observed earlier in numerical experiments. The analytical form of dependency of the critical Grashof number versus dispersion degree value is obtained. The sufficient conditions are formulated as a variational inequality, properties of which are thoroughly discussed. It is found that the form of dependency of stability characteristics (Grashof number) has regions corresponding to resonant behavior of fluctuation energy dissipation, and the sufficient stabilization is observed.