Nature of the spin dependent electron transport in carbon nanotubes with chromium atoms adsorbed at the surface has been clarified. It has been shown that the magnitude of the spin dependent trans port is determined by the relative displacement (under the effect of an external magnetic field) of the energy levels of electrons (Coulomb gaps arising in the vicinity of the Fermi level) for different spin projections.Keywords: carbon nanotubes with a chromium impurity, energy spectrum of electrons and phonons, electrical conductivity