The effect of the natural antioxidant alpha-tocopherol in a broad concentration range (10(-4) - 10(-25) M) on the viscosity characteristics and thermally induced structural transitions of a lipid bilayer of plasma membranes of murine hepatocytes in vitro has been studied. Changes in the rigidity of surface (approximately Abb) of the lipid bilayer were measured on a Bruker EMX EPR spectrometer (Germany) by the method of spin probes. Stable nitroxyl radicals of 5- and 16-doxylstearic acid, localized at different depth in the membrane served as spin probes. It was shown that the concentration dependence of the effect of alpha-tocopherol is linear and polymodal with three statistically significant increases in three ranges of its concentration: (1) in the range of traditional physiological concentrations 10(-4)-10(-9) M, (2) in the range of superlow doses 10(-9) - 10(-17) M, and (3) in the range of "imaginary" concentrations 10(-17) - 10(-25) M. The mechanisms of action of alpha-tocopherol in each of the three ranges are discussed. When studying the temperature dependences of viscous characteristics, a new thermally induced structural transition in the range of "physiological" temperatures 309-313 K for those alpha-tocopherol concentrations (including superlow ones) to which the maxima on the dose dependence curves at constant temperature of 293 K corresponded.