This article is devoted to an analysis of the reactivity of unsaturated compounds in reaction with peroxy radicals, and the relation between reactivity and the rate and selectivity of epoxidation. In the reaction of hydrogen atom detachment from olefins and addition by a double bond, the peroxy radical exhibits electrophilic properties, and the molecule nucleophilic properties. The reaction passes through a polar transition state. The introduction of a double bond into a cycloalkane and n-alkane molecule leads to an increase in the rate constant of detachment of the hydrogen atom by the peroxy radical by a factor of 10**3, and of the two double bonds by a factor of 10**5. For olefins with a rigid skeleton, the alpha -C-H bonds are completely passive.