It has been shown that in the molybdic or tungstic acid-catalyzed oxidation of petroleum sulfides with hydrogen peroxide in the presence of acetone as an additive, the specific rate of the formation and the yield of sulfoxide increase. The effective rate constants for the formation of sulfoxides characterizing the catalytic activity of molybdic and tungstic acids and the oxidizing power of an acetone-hydrogen peroxide adduct at 60A degrees C have been determined.