The catalytic properties of acids, metal compounds, and carbonyl compounds in reactions of oxidation of medium-sulfur crude diesel cut sulfides with hydrogen peroxide are examined. Comparative data on the effectiveness of these catalysts are reported. The mechanisms of formation of sulfoxides and sulfones with these catalysts are generalized. The possible mechanism of the effect of the catalysts is discussed. Optimum reactor designs which ensure minimal residence time of diesel cut sulfides in the reaction zone with effective heat and mass exchange are described.