This article addresses mathematical modeling of the reaction of inhibited organic compounds oxidation. It was proposed to solve the inverse problems of chemical kinetics by using the index method of constrained global minimization of the deviation between the calculated and experimental data. This approach allows us to use more complete information about the chemical process which, in its turn, reduces the range of possible solutions, narrows down the domain of uncertainty, and improves the quality of mathematical model of chemical reactions. The index method was applied to solving inverse kinetic problem for the reaction of n-decane oxidation in the presence of a p-oxydiphenylamine/n-decyl alcohol inhibitory composition.