The kinetics of the initiated oxidation of 1,4-dioxane in the presence of azepanobetulin and methyl-3-(hydroxyimino)-lup-20(29)en-28-oate additives has been studied. It was found that the introduction of minor additives of these substances into 1,4-dioxane oxidized in the initiated mode leads to the appearance of induction periods on the kinetic curves of oxygen absorption. It was found that the stoichiometric coefficient of inhibition f, the value of which is proportional to the number of peroxyl radicals that interact with one inhibitor molecule, resulting in a oxidation chain break, is > > 2, which is explained by the reaction of regeneration of antioxidant molecules. The possibility of participation in this reaction of the 2-hydroxy-1,4-dioxane molecule, which is an intermediate product of 1,4-dioxane oxidation, is discussed. Oxidation of this product leads to the formation of hydroxyperoxyl radicals, which, according to a previously established mechanism, are capable of reducing the original antioxidant molecule from its radical in the act of chain termination. A reaction mechanism is formulated that satisfactorily describes the experimental results. A mathematical model of the reaction was formulated, the study of which, with the help of the << ChimKinOptima >> software complex, made it possible to satisfactorily describe the experimental kinetic curves as well as to obtain the kinetic curve of the accumulation of hydroperoxide, the primary product of 1,4-dioxane oxidation, which was not observed in the experiment, and to determine the reaction rate constants included in the proposed mechanism.