For the thermal and thermooxidative degradation in fullerene (C-60, C-70)-Polymer (PMMA, polystyrene) systems, concentration limits were observed for the stabilizing effect of fullerenes that depend on the solubility of the fullerene in a polymer: for polystyrene and PMMA, these values are 4 x 10(-3) and 8 x 10(-3) Mol/kg of fullerene, respectively. Thermal and thermooxidative degradation occurred in the presence of fullerenes were also characterized by the existence of temperature limits for the effective action of inhibitors. For polystyrene-based systems containing C-60 or C-70, the temperature limit of thermal degradation was 380degreesC; for PMMA-based systems, this parameter amounted to 339 and 336degreesC for C-60 and C-70, respectively. For the thermooxidative degradation of these polymers and a polycarbonate, the temperature range 335-340degreesC was the highest temperature limit for fullerene C-60 as an antioxidant, which was much lower than 370degreesC, the temperature corresponding to the onset of the intense oxidation of fullerene.