The purpose of this work was to examine the interaction of graphene-like nanoclusters with fragments of polymers of the same nature, but somewhat different structure, for example, polyethylene (PE) and polypropylene (PP) by means of quantum chemistry. By method of density functional theory with the exchange-correlation functional B3LYP, the basis set 6 - 31 G (d, p) and the Grimme’s dispersion correction, the energy values have been calculated of interaction between nanocarbon fragments and oligomers of PE and PP, 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 surface of the graphene and carbon nanotubes (CNT). In order to take into account the dimensional effect of the surface of the nanotube fragment model on the interaction energy, in addition to the above described, two larger models were used, with the general formula C₅₄H₁₈ and C₉₆N₂₄. It has been found that the interaction energy of nanocarbon fragment with an oligomer of PP is greater, compared with PE, which is consistent with the experimental data on melting temperatures of pure polymers and nanotube-polymer composites. The polymer with a surface of nanocarbon fragment forms an intermolecular complex not bound covalently and retained by intermolecular dispersion forces. Oligomers of polymeric matters and carbon surfaces in formed nanocomplex are placed closer to each other than separate polymeric links between them.