The kinetics and composition of the products of degradation of hydrogen peroxide, ethylbenzene, and cumene hydroperoxides at 343 K in the presence of the styrene epoxide + p-toluenesulfonic acid binary system in a ten-butanol solution with 10 vol % chlorobenzene in an argon atmosphere were studied. The values of the partial reaction orders of hydroperoxide consumption, namely, the zero order in the epoxide and the first in the acid, are the same as the corresponding parameters of the reactions of oxygen uptake and benzaldehyde formation in the oxidation of the binary system. A mechanism of the oxidation of the binary system is proposed, which involves the intermediate formation of a carbene, which destroys hydroperoxides in an inert atmosphere.