Nanosized systems of DOX with antitumor activity on the base of micelle-like particles of amphiphilic thermosensitive copolymers of N-vinylpyrrolidone (VP) with triethylene glycol dimethacrylate (TEGDM), and N-vinylpyrrolidone and methacrylic acid (MAA) with TEGDM were explored. They were investigated in aqueous solutions by electron absorption spectroscopy, dynamic light scattering and cyclic voltammetry. Experimental data and quantum-chemical modeling indicated the formation of a hydrogen bond between oxygen-containing groups of monomer units of the copolymers and H-atoms of OH and NH2 groups of DOX; the energies and H-bond lengths in the considered structures were calculated. A simulation of TDDFT spectra of DOX and its complexes with the VP and TEGDM units was carried out. Electrochemical studies in PBS have demonstrated that the oxidation of encapsulated DOX appeared to be easier than that of the free one, and its reduction was somewhat more difficult. The cytotoxicity of VP-TEGDM copolymer compositions containing 1, 5 and 15 wt% DOX was studied in vitro on HeLa cells, and the values of IC50 doses were determined at 24 and 72 h of exposure. The copolymer compositions containing 5 and 15 wt% DOX accumulated actively in cell nuclei and did not cause visual changes in cell morphology.