The competition among the three different elementary second-order processes involving the radicals A and B,is frequently established in many combustion and atmospheric chemistry systems. The analytical resolution of the above mechanism for k AB = 2k AA and k AB = 2k BB , that is, for a crosscombination ratio φ = k AB /(k AA k BB ) 1/2 = 2, is well-known, but it has been claimed not to exist for φ = 2. In the present paper an analytical resolution of the system (1)- (3), performed under the condition k AB = 2k AA and k AB = 2k BB , leads toThe mathematical procedure leading to this equation and the equation itself are valid independently of the nature of the products of the reactions (1), (2), and (3), that is, recombination or disproportionation products, provided that the reactants and the order of the reactions remain the same.