The one-electron reduction potential in water of 28 alkyl peroxyl radicals and 10 aromatic peroxyl radicals have been estimated from previously published kinetic data on electron-transfer reactions. The kinetic data were calibrated against thermochemical data on peroxyl radicals. From the estimated one-electron reduction potentials and acidity data on some hydroperoxides, the pK(a) values of the corresponding hydroperoxides were estimated. The homolytic O-H bond dissociation energies of the hydroperoxides were calculated from the estimated one-electron reduction potentials and pK(a) values. The results have been summarized in linear free energy relationships based partly on an operational substituent constant scale derived in this work. In addition the ionization potentials of 16 peroxide anions, the absolute hardness and electronegativity of the corresponding peroxyl radicals and the O-H bond dissociation energies of the corresponding hydroperoxides have been calculated by AM1 semiempirical quantum chemical calculations. These calculations were shown to be unreliable.