A scheme for calculating populations of excited levels and intensities of spectral lines in the positive column of helium discharges at intermediate pressures (p>5 Torr) is proposed. The electron distribution obtained from the Boltzmann equation is taken into account. The distribution is strongly non-Maxwellian for electrons of energy more than 19.8 eV. Concentrations of atoms on excited levels (n=2,3,4,5) are obtained from balance equations for the population of those levels. The concentration of level 23S is the highest. The concentration of 21S is much less than that which would exist in the case of quasithermodynamic equilibrium between levels 23S and 21S. The population of higher levels (n>2) is determined by excitation from levels 23S and 21S. For singlet levels the excitation from level 21S is important. Population inversion is obtained between levels 31P-31D, 41P-41D, 51S-41P, 43S-33P, 53S-43P and 53P-43D.