Two decoupling procedures are proposed within the framework of the hyperspherical coordinate approach in order to reduce the number of states in the close-coupling calculations and to clarify the reaction mechanisms. Sharply avoided adiabatic states are diabatically connected and relabeled without any diabatic coupling there. This is named diabatic decoupling and is useful for decoupling two manifolds of states belonging to different categories. Furthermore, the number of states is reduced in such a way that only a limited number of adjacent adiabatic states are taken into account in the close-coupling calculations for each relevant state. This is called adiabatic decoupling scheme. These reductions of the number of states enable us to analyze reactions in terms of nonadiabatic transitions at avoided crossings among the small number of adiabatic potential curves. The method is applied to O(P-3) + HCl --> OH + Cl and Cl + HCl --> HCl + Cl. The idea of vibrationally nonadiabatic transitions at avoided crossings together with the concept of potential ridge introduced in our previous paper can untangle the congested potential curves and clarify reaction mechanisms.