A self‐gravitating, infinite cylinder of conducting, homogeneous, incompressible fluid in an axial magnetic field is considered with Hall effect included. In the case of axisymmetric modes, an asymptotic analysis for small, nonzero Hall current indicates a destabilizing effect ofO(&egr;), where &egr; is the perturbation parameter. It appears that the increased instability is due to the electron‐ion diffusion current, which contributes a radial Lorentz force that is absent in the single‐fluid theory. This radial Lorentz force increases the tendency for the cylinder to break up into lengths defined by the perturbation wavenumber.