The competition between intramolecular and bimolecular reactions of alkoxyl radicals formed from artemisinin was theoretically analyzed. The enthalpies of these reactions were calculated. The activation energies and rate constants of reactions of intramolecular hydrogen atom transfer, decyclization, and decomposition of alkoxyl radicals of artemisinin and several its derivatives, as well as the activation energies and rate constants of reactions of these radicals with the C-H, S-H, and O-H bonds in biological substrates and their analogs were calculated by the intersecting parabolas method The fastest reactions of artemisinin alkoxyl radicals were identified. The full kinetic scheme of transformation of these radicals was proposed. Artemisinin radicals with the free valence on the carbon atom are predominantly formed due to the transformation of the artemisininoxyl radicals.