Catalytic fullerenol C₆₀ (OH)₂₄ action on Chlorella Vulgaris growth in the conditions of limited resource growth base and in the conditions of oxidative stress are reported. Chlorella growth or oppression were investigated in open transparent in the visible area cylindrical polystyrene test tubes at room temperature under illumination by standard incandescent lamp for the period 9 days. Catalyst concentration were varied in the range 0.01 – 1.0 g/dm³ . Oxidative stress was organized by the addition of hydrogen peroxide with the concentration 1.0 g/dm³ . Chlorella Vulgaris concentrations were determined by the method of turbidimetry – by the determination of optical density of scattered light in the direction of propagation of the incident beam at wavelength 664 nm. Obtained kinetic data were processed by the method of formal classical kinetics. The pseudo-order of the process Chlorella Vulgaris growth in the conditions of limited resource, according to Chlorella, is −2; the curve of the dependence of Chlorella concentration against time is concave at all fullerenol concentrations. The pseudo-order of the process Chlorella Vulgaris suppression in the conditions of oxidative stress, according to Chlorella, is +2, the curve of the dependence of Chlorella concentration against time is convex at all fullerenol concentrations. The kinetics of Chlorella Vulgaris growth in the conditions of limited resource was also processed by model Verhulst equation of logisitic growth, and this equation describes the kinetics as accurately and adequately as possible. The authors have established, that in the case of the conditions of limited resource, fullerenol at low concentrations (less than 0.1 g/dm³ ) catalyzes-accelerates Chlorella growth and at higher concentrations (0.1 – 1.0 g/dm³ ) inhibits Chlorella growth. For the conditions of oxidative stress, authors have established, that at all fullerenol concentrations, it considerably inhibits suppression-depopulation of Chlorella processes, so fullerenol proves enough strong anti-oxidant action. It was demonstrated, that Verhulst equation maybe satisfactory used for the description of different natural process.