The processes of modifying the surface of multi-walled carbon nanotubes growing with polar substances – carboxyl, alcohol, hydroxyl, quaternary ammonium salt – have been studied. With the combination of an oxidizing mixture of hydrogen peroxide, nitric and sulfuric acids, a technology has been developed for the carboxylation of carbon nanotubes at 70 °C, which results in minimal formation of amorphous carbon and increases the content of carboxyl groups on a surface to 5.5 %. The reaction of carboxylated carbon nanotubes with triethanolamine has led to the tubes with the surface modified by a quaternary ammonium salt. Modification of carbon nanotubes by ethyl hydroxyl groups has been carried out with the participation of a free-radical initiator in an ethanol medium. It has been shown that the number of defects that occur during formation of chemical bonds in the process of functionalization, as well as their nature, are predominantly determined by the initial defects of nanotubes and do not depend on the processing of the nanocarbon material. A study of the thermal-oxidative stability of the original and modified carbon nanotubes has been carried out. The original nanotubes are the most stable, heated in air up to 520 °C. Thermal stability for the investigated modified nanotubes decreases in the series: multi-walled nanotubes with carboxyl groups on the surface, with alcohol hydroxyl groups modified by a quaternary ammonium salt, in which oxidation begins at 400 °C. Grafting alcohol hydroxyl groups on the surface of multiwalled carbon nanotubes is of considerable interest for the formation of a sorption material with a developed surface, capable of covalently binding metal ions due to hydroxyl groups, similar to complexing agents such as ethylene glycol or pyrocatechol. The surface modification of carbon nanomaterials with polar groups leads to good sorption properties for the heavy metal ions. The extraction of zinc and copper ions in the case of carboxylated nanotubes is up to 98 %.