The reactions of methyl and methylperoxyl radicals derived from dimethyl sulfoxide (DMSO) with hydrogen peroxide, peroxymonocarbonate (HCO4−), and persulfate were studied. The major reaction observed for the hydroperoxides was the abstraction of the hydrogen atom by the radicals. The radicals interact with a lone pair of electrons on the peroxide to produce methanol and formaldehyde. Furthermore, the results indicate that in RO2H and RO2R′, electron-withdrawing groups cause a considerable increase in the reactivity of the peroxides towards the radicals and not only towards nucleophiles. The HO2./O2.− and CO3.− radicals react with DMSO to produce methyl radicals. Thus, the formation of the .CH3 radicals in the presence of DMSO is not proof of the formation of the .OH radicals in the system. These reactions must be considered when radical processes, such as in biological and catalytic systems, are studied. Especially, the plausible role of HCO4− ions in biological systems as a source of oxidative stress cannot be overlooked.