Alkanesulfonic peracids RSO4H effectively oxidize olefins to the corresponding epoxides. The kinetics and mechanism of this reaction are studied. It was shown that both the monomer and dimer form of the peracid act as oxidizing agents. The dependence of the weight constant of the reaction of monomer RSO4H with substituted acyclic olefins on the structure of the latter is described by the Taft equation. A linear correlation is established between log k2 and the inductive constants of the substituents on the oxygen atom in the peracid.