Carbon nanotubes (CNTs) and carbon nanofibers (CNFs) have electron affinities similar to those of fullerenes C60 and C70 and they are therefore capable of acting as radical scavengers in free radical chain reactions, including polym- erisation and the thermo-oxidative degradation of polymers. It is assumed that the CNTs and CNFs used as integral part of polymer composites are able to exhibit an antioxidant effect in these materials because of their radical accepting capacity. To examine this presumption the antioxidative activity of original and purified commercial multiwall carbon nanotube MWCNT and carbon nanofibre of platelet structure CNF-PL has been studied by means of a model oxidation reaction of cumene initiated (2,2'-azobisisobutyronitrile, AIBN) in liquid phase. This model reaction was designed to simulate the thermo-oxidative processes in carbon-chain polymers and allows comparison and transfer of obtained results to a polymer system. Kinetic measurements of oxidation rates showed that the effect of inhibition for the model oxidative reaction in the pres- ence of the original and purified MWCNT and CNF-PL strongly depends on the presence of metals (Co, Fe) in the nanoparticles. Rates of oxidation Wo2 (CNT;CNF) observed for the unrefined samples are result of the two competing rates - rate of inhibition Winh.(CNT; CNF) caused by structures of the CNT or CNF and the rates of initiation Wi(M) due to the follow- ing interaction: ROOH + M (Co;Fe) i.e, Wo2 ~ W inh (CNT;CNF) + Wi(M). The effective rate constants for the addition of cumyl radicals (R� ) to MWCNT and CNF-PL have been determined. These constants reduced to the same concentration (0.5wt.%) and temperature (60 o C) units have magnitudes: k1(MWCNT) (MWCNT) = (2.8 ± 0.3) � 10 4 s -1 and k1(CNF) (CNF) = (6.0 ± 1.0) � 10 3 s -1 . Thus, the effective rate constant, reflecting the antioxidative activity for the CNT, is five times higher than that for the CNF, is about equal to the rate constant for HAS Chimassorb 2020: k1(Chim.2020)(Chim. 2020) = (2.2 ± 0.3) � 10 4 s -1 , is ten times less than that for the HAS Chimassorb 119FL: k1(Chim.119FL)(Chim. 119FL) = (2.8 ± 0.3) � 10 5 s -1 and is about forty times less than that for the case of fullerene C60: k1(C60)(C60)(353K) = (1.2 ± 0.2) � 10 6 s -1 .