It is well established that alpha-tocopherol, TocH, is an outstanding lipid-soluble, peroxyl radical trapping antioxidant in homogeneous systems. It is also well established that TocH functions as a prooxidant in human low-density lipoprotein, LDL, subjected to attack by peroxyl radicals generated in the aqueous phase by, for example, thermal decomposition of the azo compound, ABAP. This tocopherol-mediated peroxidation, TMP, of LDL involves a three-step chain reaction, one step being hydrogen atom abstraction from the LDL lipids by the tocopheroxyl radical, Toc*. The occurrence of TMP has been attributed to three factors, (i) translocation by TocH of radical character from the aqueous phase into LDL lipid, (ii) isolation of the water-insoluble Toc* in the LDL particle in which it is formed for times sufficient to permit it to react with the lipid, and (iii) the small lipid volume of LDL which ensures that no particle can contain more than a single radical for a significant length of time. This consensus view of TMP implies that it should occur in any TocH-containing dispersion of small lipid particles. However, the present examination of the kinetics of the ABAP-initiated peroxidation of small unilamellar vesicles, SUVs, made from palmitoyllinoleoylphosphatidylcholine and cholesterol with a composition designed to mimic the surface coat of LDL, has shown that TocH functions as an antioxidant in such systems and that TMP does not occur under conditions where it would have occurred if the particles had been LDL. Several possible reasons for the kinetic differences between SUVs and LDL have been considered and ruled out by experiment. It is concluded that TMP can occur in LDL because these particles contain a lipid core in which the Toc* radical "hides" for much of its lifetime well away from the peroxyl radicals in the aqueous phase. In contrast, because SUVs have no lipid core, the Toc(*) radical is always "exposed" and available to aqueous peroxyl radicals with which it reacts rapidly and is destroyed before it can abstract a hydrogen atom from the lipid.