The reaction mechanisms of the O-O cleavage of organic peroxides, hydrogen peroxide, hydroperoxides, dialkyl peroxides, peracids, peroxyesters, and diacyl peroxides, have been explained on the basis of their HOMO and LUMO and on the basis of the potential surfaces along the reaction paths. The discussion covers the electronic structure and conformation of the peroxides, the characteristics of HOMO and LUMO of the peroxides, the reaction with nucleophiles and with electrophi-les, homolytic decomposition process, radical-induced decomposition, and the electronic structure of the radicals produced from the O-O cleavage. © 1979, The Society of Synthetic Organic Chemistry, Japan. All rights reserved.