The kinetic characteristics, mechanisms of activity, and relationship between the antioxidant activity and the molecular and supramolecular structure of fullerene C60 and some of its N-monosubstituted amino acid derivatives have been studied. The introduction of an amino acid substituent in the C60 fullerene molecule led to an increase in its antiradical activity in the free radical oxidation of a water-soluble target (fluorescein). The mechanism of the antioxidant activity of amino acid derivatives of fullerene is not associated with the hydrogen atom transfer, electron donation, or catalysis of peroxide decomposition. It was demonstrated that the structure of the amino acid substituent does not affect the antiradical properties, which are thus determined only by the effective total surface area of the nanoparticles of the fullerene C60 derivatives and increase when their size decreases. This surface can be characterized as nanowalls on which the radical death occurs. A change in the concentration of the compounds in solution does not lead to a change in the relative antiradical activity and hence in the nanoparticle size. The results of this study are important for understanding the biological activity of this group of compounds.