An examination has been made of the hydroperoxide and peroxide epoxidation of 3-methylbut-1-ene. The indices of hydroperoxide epoxidation are given. A mathematical model of the production of tert-amyl hydroperoxide by the liquid-phase oxidation of isopentane has been developed. The optimum conditions have been selected for the epoxidation of 3-methylbut-1-ene to the corresponding oxide and diol under interphase catalysis conditions.