Dialkyl and diaryl sulfoxides are oxidized to sulfones by hydrogen peroxide using methyltrioxorhenium as the catalyst. The reaction rate is negligible without a catalyst. The kinetics study was performed in CH3CN-H2O (4:1 v/v) at 298 K with [H+] at 0.1 M, conditions which make the equilibration between MTO and its peroxo complexes more rapid than the oxygen-transfer step. The values for the rate constant for the oxygen-transfer step lie in the range 0.1-3 L mol(-1) s(-1). The rate constants were significantly smaller than for the oxidation of sulfides to sulfoxides. A study of ring-substituted diaryl sulfoxides yielded kinetics results that are consistent with nucleophilic attack of the sulfur atom on the peroxide oxygen group since rho = -0.65, The results cited refer to the reactions of the diperoxo from the catalyst, MeRe(O)(eta(2)-O-2)(2)H2O. The monoperoxo complex showed no measurable reactivity toward sulfoxides, in contrast with the situation for nearly every other substrate. That unusual finding suggests a hydrogen-bonded interaction between the substrate and the diperoxorhenium compound which cannot exist with the monoperoxo compound.