Homolytic addition reaction of N-halogenosulphoximides, i.e. diphenyl-N-chlorosulphoximide (1), diphenyl-N-bromosulphoximide (2), and methylphenyl-N-chlorosulphoximide (3), to olefins such as t-butylethylene and cyclohexene under both u.v. irradiation and thermolysis in the presence of a radical initiator was found to afford the corresponding N-alkylated sulphoximides, which are presumed to be formed via the initial addition of the sulphoximidoyl radical. Meanwhile, homolytic bromination of toluene with N-bromosulphoximide (2) proceeded readily by u.v. irradiation, or by thermal reaction in the presence of a radical initiator, to afford benzyl bromide. However, chlorination of toluene was sluggish with N-chlorosulphoximides (1) and (3). α-Bromination was interpreted in terms of a chain process involving bromine molecules like the ‘Goldfinger mechanism,’ but not via that involving the sulphoximidoyl radical.