The search for new active compounds with the antioxidant (anti-tumor) activity, as well as the development of theoretical methods of analysis of the mechanisms and kinetics of antioxidant (antitumor) activity for a number of the natural and synthetic chemicals, is an important task. Vitamin E (α-tocopherol) is the major lipid-soluble antioxidant of lipoproteins and biomembranes [1]. As a phenolic compound (Ph-OH), its antioxidant activity relies on the ability to donate the hydrogen from the hydroxyl group of the chromanol ring to the reactive lipid chain-propagating radicals such as the peroxyl radicals (LOO•) to yield the lipid hydroperoxide (LOOH) and vitamin E phenoxyl radical (Ph-O•) [2]. The efficacy of vitamin E as an antioxidant not only depends on its reactivity toward damaging radicals [1], but also on the relatively stable nature of its radical due to delocalization of the unpaired electron about the chromanol ring.     Fig. 1. a) – The α-tocopherol;  b) – The synthetic α-tocopherol derivative with the short side chain;  c) – The scheme used for the definition of reaction kinetics.   Fig. 2. The concentration time dependences for the intermediate complex X(t), product P(t) and substrate S(t).   Department of Biochemistry of vitamins and coenzymes of the A.V. Palladin Biochemistry Institute of NAS of Ukraine developed a technology for a producing of high-performance derivative – an analog of vitamin E for the manufacture of bioactive, or dietary supplements. The model experiments on animals have demonstrated the ability of a vitamin E derivative with a shortened side chain to reduce the tumor size and number of metastases even more effective than the vitamin E. Thus, the inhibition of cytochrome C peroxidase activity increases with a decreasing of the length of side chain of α-tocopherol by more than an order.     In this paper within the framework of a simple kinetic model to perform the comparative analysis of cytochrome C peroxidase reaction involving a vitamin E and its synthetic derivative with the truncated side chain as the inhibitors for the radical chain-propagating reactions. Simulation of the kinetics of reaction was performed using the reaction scheme shown in Fig. 1c. This eventually corresponds to the system of differential equations describing the reaction kinetics, a qualitative behavior of the concentration time dependences for the intermediate complex X(t), product P(t) (vitamin E phenoxyl radical) and substrate (vitamin E) S(t) is shown in Fig. 2. The quantitative estimates for the reaction rates are taken from the results of experiments and quantum chemical calculations.