Earlier studies established that dimethyldioxirane (1a) reacts with sulfides 2 in two consecutive concerted electrophilic oxygen-transfer steps to give first sulfoxides 3 and then sulfones 4. The same sequential electrophilic oxidation model was assumed for the reaction of sulfides 2 with the strongly electrophilic methyl(trifluoromethyl)dioxirane (1b). In this paper we report on a systematic and general study on the mechanism of the reaction of simple sulfides 2 with DMDO (1a) and TFDO (1b) which provides clear evidence for the involvement of hypervalent sulfur species in the oxidation process. In the oxidation of sulfides 2a-c, diphenyl sulfide (2d), para-substituted aryl methyl sulfides 2e-i, and phenothiazine 2k with 1b, the major product was the corresponding sulfone 4, even when a 10-fold excess of sulfide relative to 1b was used. The sulfone:sulfoxide 4:3 ratio depends among other factors on the dioxirane la or 1b used, the sulfide substitution pattern, the polar, protic, or aprotic character of the solvent, and the temperature. The influence of these factors and also deuterium and O-18 tracer experiments performed allow a general mechanism to be depicted for these oxidations in which the key step is the reversible cyclization of a zwitterionic intermediate, 6, to form a hypervalent sulfur species, 7. The classical sequential mechanism which establishes that sulfides are oxidized first to sulfides and then to sulfones can be enclosed in our general picture of the process and represents just those particular cases in which the zwitterionic intermediate 6 decomposes prior to undergoing ring closure to afford the hypervalent sulfurane intermediate 7.