We consider the nonlocal theory of a positive column in a glow discharge in two cases, where the mean free path of charged particles is either greater than the discharge tube radius (the free-flight regime) or much less than the radius (the collisional regime). The great bulk of electrons, which determines the density and the discharge current in the axial direction, appears to be trapped by the radial field of a positive column. The electron flux to the wall, which compensates for the ionization in a volume, is determined by fast electrons with energies of the order of wall potential, which are able to leave in a loss cone. The electron kinetic equation, which is solved by averaging it over the radial transits for the two regimes considered, permits us to obtain the electron density and the ionization rate. Thus, we develop the theory of a positive column for the non-Boltzmann electron distribution in the radial field. Under the free-flight regime, this theory is developed by analogy with the Langmuir-Tonks one. Under the collisional regime, the spatial distribution of the potential is obtained from the ion motion equation with the ambipolar diffusion coefficient, which depends on the radial coordinate. The concrete calculations are carried out for the xenon discharge under the free-flight and collisional regimes. The theoretical calculations are compared with the results of experiments on the measurements of the electric field and the densities of metastable and resonance xenon atoms.