The results of the study on the properties of carbon nanotubes-polymer nanocomposites have shown that the use of nanotubes (CNT) to fill the polymer matrices of different species significantly alter their physical properties compared to the original polymers. However, the influence of CNT on the properties of nanocomposites obtained at the molecular level has not been completely ascertained yet. Therefore, the purpose of this work was to examine the interaction of CNT with fragments of polymers with the same nature, but the different structure, for example, polyethylene and polypropylene using quantum chemistry.By method of density functional theory with the exchange-correlation functional B3LYP, the basis set 6-31G(d,p) and the Grimme dispersion correction, the energy values have been calculated of interaction between carbon nanotube fragments and oligomers of polyethylene and polypropylene, the most probable structures of their intermolecular complexes being optimized.A graphene-like plane of 40 carbon atoms and 16 atoms of hydrogen was chosen as a model for the outer surface of the multi-walled nanotubes (MWNT). In addition to the above described, two larger models were used, with the general formula C 54 H 18 and C 96 H 24 in order to take into account the dimensional effect of the surface of the nanotube fragment model on the interaction energy.It has been found that the interaction energy of a carbon nanotube fragment with an oligomer of polypropylene is greater, compared with polyethylene, which is consistent with the experimental data on melting temperatures of pure polymers and nanotube-polymer composites.The polymer with an outer surface of a carbon nanotube forms an intermolecular complex do not bound covalently and retained by intermolecular dispersion forces. Oligomers of polymeric matters and nanotube surfaces in nanocomposites formed are located closer to each other than separate polymeric links between them.