Rates and selectivities for the oxidation of various organosulfur compounds with tert-butyl hydroperoxide were measured on CoAPO-5 (APO = aluminophosphate; Co/P = 0.05), Co/H-Y (Co/Al = 0.15), and MoO(x)/Al2O3 (15 % wt MoO3). Rates increased with increasing electron density at the sulfur atom (methyl phenyl sulfide>diphenyl sulfide>4-methyldibenzothiophene>2,5-dimethyl thiophene). Rates (per metal atom) were significantly higher on CoAPO-5 than on Co/H-Y, MoO(x)/Al2O3, or homogeneous Co acetate catalysts. Small amounts of sulfoxides (1-oxide) were detected on all catalysts at low reactant conversions, together with their corresponding sulfones; at higher conversions, only sulfones (1,1-dioxide) were detected, indicating that the oxidation of sulfoxides is much faster than for organosulfur reactants in the sequential oxidation pathways prevalent on these catalysts. Framework Co cations were not leached from CoAPO-5 during the oxidation of 4-methyldibenzothiophene, but most exchanged Co cations in H-Y and >20 % of Mo cations in MoO(x)/Al2O3 were extracted during these reactions. The fraction of redox-active Co cations in CoAPO-5 and Co/H-Y was measured by reduction-oxidation cycles using H2 and O2 and by UV-visible spectroscopy. This fraction was much larger in CoAPO-5 (0.35) than in Co/H-Y (0.01), consistent with the higher oxidation rates measured on CoAPO-5 and with the involvement of redox-active species in kinetically-relevant steps in catalytic oxidation sequences. Redox-active Co cations at framework positions within accessible channels are required for catalytic activity and structural stability during oxidative desulfurization, whether hydroperoxides are used as reactants or as intermediates (when O2 is used as the oxidant).