Synthesis of cluster Rhenium compounds with different organic ligands was elaborated [Shtemenko A.V., 1994-2005]. In our previous works it was shown that binuclear Rhenium compounds with common formula Re2(RCOO)nX2, where R = tetraisobutyric, n = 4, Х = Cl, (Re1); R = GABA (cis), n = 2, Х = Cl (Re2); AdCOO- (adamantancarbonic), X = Cl, n = 2 (Re3), had perfect antitumor action in two kinds of experiments: a) with use of substances alone; b) with use of rhenium substances together with well-known cytostatics, changing the velocity of tumor growth and being as antioxidants in blood of tumor-bearing animals. In this work we try to analyze obtained data and to determine further synthetic directions. The dependence of antioxidant properties of a substance from ligands situated around the cluster rhenium fragment Re2 6+ was detected. Antioxidant properties of cluster rhenium compounds depended on the ability of ligands to stabilize possible radical state as a quadruple bond served like a trap for radicals. These results coincided with results obtained in experiments in vitro with a stable triphenylverdazyle-radical, where dichlorotetra-μ-ibutyratodirhenium( III) distinguished the radical very effectively and with the velocity comparable with natural antioxydant, tokopherole. Antitumor activity of cluster rhenium compounds showed another dependence from ligand structure and was the best for the compound with the formula [cis-Re2(GABA)2Cl5(H2O)]Cl·H2O (GABA = γ-aminobutyric acid residue) - (Re2); in experiments of a) type. These data open opportunity to synthesize cluster rhenium compounds with ligands from one hand capable to distinguish free radicals and from another - bearing amino acid or peptide residue whiceh could be responsible for specific interactions with cell molecules. In experiments of type b) the best was Re1 with symmetric position of tetraisobutyric radical. In the experiment with cisplatin together with reducing of tumor size, introduction of the rhenium substance led to practically normal morphological picture of red blood cells, even to reduction of quantities of damaged cells. Presented data concerning normalization of antianemic state by rhenium substances were not surprising as close results have been obtained in the experiments with chemically induced hemolytic anemia, where such properties of cluster rhenium compounds were explained by a quadrupol Re-Re bond in the structure of such substances, which may work as a trap for free radicals. Due to such chemical features rhenium substances were able to support normal state of red blood cells that is very important during development of malignancy and application of cisplatine.