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Free radicals participate in two important processes in the life bodies: cell signaling and cell injury. Mean¬while, their extreme chemical reactivity makes imposs¬ible to determine directly their content and investigate their reaction mechanisms by routine biochemical technique, such as substrate isolation, purification, analysis etc. Fortunately, we can follow many impor¬tant radical-mediated reactions by measuring chemilu¬minescence, accompanying those reactions. We have elaborated an instrument SmartLum, specially adopted for measuring the non-stationary reaction kinetics, very sensitive and supplied with devices for thermostating, solution adding during the reaction, stirring and on-line data processing and storage by using a software PowerGraph (http://www.powergraph.ru/). The chemiluminescence kinetic curves were measured in different experimental conditions and compared with the curves calculated with a computer program Kinetic Analyzer, specially designed in collaboration with Dr. Dmitry Izmailov in our lab for complex reaction kinetic simulation. By using the initial concentrations of all reaction substrates and varying the reaction rates of all the reactions proposed, we compared the experimental and calculated curves. The coincidence of these curves is considered as an evidence that the reaction scheme and the rate constants are valid. Recently a student Leonid Batov has invented a software to fit automatically the reaction rates in the assumption that the reaction scheme is known. The reaction schemes of the chain lipid peroxidation reactions in the presence of Fe2+ ions, antioxidants reactions in this system, reactions of luminol oxidation by H2O2 catalyzed by peroxidases and cytochrome c/ cardiolipin complex, and antioxidant reactions in the TRAP method were investigated by using the kinetic chemiluminescence method and the results are dis¬cussed, along with the mechanism of the antioxidant reactions and the antioxidants' antiradical activities.