Theoretical analysis for the stability of a diffusion dominated positive column between coaxial cylinders in the presence of an axial magnetic field is carried out under the assumptions of quasi-neutrality of charges and no sheath at the walls. Self-consistent infinitesimal perturbations of plasma density and electric potential, which satisfy the linearized governing equations to the same degree of approximation are used to derive the dispersion relation. The perturbations associated with aximuthal modes m ≤ 0 are stable for any gap size and plasma parameters. The stability of non-axisymmetric perturbations is studied for different gaps. It is found that the presence of inner cylinders increases the stability of a magnetized positive column and m = 2 defines the region of stability when the ratio of the radii of the inner and outer cylinders is less than 0·5. In the case of narrow gaps, higher and higher modes are excited. The minimum non-dimensional axial electric field at which the magnetized positive column between coaxial cylinders becomes unstable for different gaps is also determined.