Application of the advanced Hook-Jeeves method for the solution of systems of nonlinear equations has led to determination of the equilibrium composition of the product mixture formed in the reaction of oxidizing ammonolysis of methane (OAM). It is shown that the composition crucially depends on the number of the considered parallel and sequential reactions. It is established that no thermodynamic restrictions exist both for the formation of formic acid in the course of the OAM reaction and for the subsequent conversion of formic acid to hydrogen cyanide.