The kinetics of the oxidation of dimethylsulfoxide by oxohydroxoosmate(VII1) complex ions in alkaline media follow pseudo-first-order disappearance in Os(VII1). The values of the observed pseudo-first-order rate constant are linearly dependent on initial dimethylsulfoxide concentrations in a fortyfold range, and increase with increasing [OH-], leveling off at higher relative [OH-]. The results are interpreted in terms of outer sphere interactions involving dimethylsulfoxide and various species of the Os(VII1) complex. The more nucleophilic dihydroxotetraoxoosmate(VII1) ion reacts about 50 times faster than the trihydroxotrioxoosmate(VII1) species.