Some features of processes occurring during the polarization of smooth platinum electrode in 10.0 M methanesulfonic acid (CH3SO3H) solution at high anodic potentials are studied by the cyclic voltammetry method. On cyclic voltammograms of smooth platinum electrode in concentrated methanesulfonic acid solution, well-pronounced oxidation waves are observed at potentials E = 2.0–2.5 V and E = 2.9–3.7 V. The electrochemical processes occurring in 10 M CH3SO3H solution within the E = 2.0–2.5 V potential range are shown to be associated with discharge of water molecules; the broad oxidation wave within the potential range of E = 2.9–3.7 V is related to the formation of peroxide compounds. Based on the electrochemical measurements and analysis of products of preparative electrooxidative electrolysis, the formation of a complex organosulfur peroxide compound, bis(methanesulfonyl) peroxide CH3S(O)2OOS(O)2CH3 (other names: dimethyl disulfoperoxide, or dimethanesulfonyl peroxide, or dimesylate peroxide) is established. Anodic oxidation mechanism in concentrated CH3SO3H solutions is proposed. It is supposed that the formation of the peroxide compound is associated with the participation of mesylate-radicals that dimerize at the smooth platinum anode and then are desorbed into the solution bulk.