The relatively low lying first electronic excited states of peroxyl radicals are suggested to play a direct role in determining the rate of their addition to alkenes, with there being, in the vicinity of the transition state, an unavoided crossing of C s symmetry of the ground and first excited states. If there is no charge transfer between radical and alkene during the formation of the adduct, then the barrier height is approximately equal to the energy required to excite an isolated peroxyl radical to its first excited state; with charge transfer, the activation energy for the addition is lowered in proportion to the energy released by the charge transfer. It is also suggested that for the specific case of hydroperoxyl radical addition to ethene, this description is compatible with the generally accepted mechanism for the reaction of ethyl radicals with molecular oxygen whereby the resulting ethylperoxyl radical can decompose to ethene and a hydroperoxyl radical via a cyclic 2 A transition state. Electron affinities, ionisation energies, absolute electronegativities and hardness of acetylperoxyl, hydroperoxyl, methylperoxyl, ethylperoxyl, iso-propylperoxyl and tertbutylperoxyl radicals have been calculated at the G2MP2 level.