In order to therapeutically destroy cancer neoplasms, chemotherapy or radiotherapy are commonly used. In the isotope medicine, however, medical isotopes of the short-lived radionuclides are injected into the tumor (59Fe, 90Y, 95Zr, 99mTc, 106Ru, 114*In, 147Eu, 148Eu, 155Eu, 170Tm, 188Re, 210Po, 222Rn, 230U, 237Pu, 240Cm, 241Cm, 253Es). Binary, or neutroncapturing, technology is a technology developed for the selective effect on malignant tumors and using a tropic to tumors preparations containing non-radioactive nuclides (10B, 113Cd, 157Gd et. al.). Triadic technology is a sequential administration of a combination of two or more separately inactive and harmless components tropic to tumor tissues that can selectively accumulate in them or react with each other to destroy tumors under certain external impacts. The aim of this work is the quantum-chemical modeling of the electronic structure and the analysis of the thermodynamic stability of the new methotrexate containing nanoscale fullerenolic radionuclide tumor-fghting agents. The need for preliminary studies on modeling of such objects is caused by the very high labor intensity, cost and complexity of their practical preparation.