The influence of strong self‐electric fields on the ion resonance instability is examined for a cylindrical nonneutral plasma column immersed in a uniform axial magnetic fieldB0eˆz. The analysis is carried out within the framework of a macroscopic cold‐fluid model, and electrostatic stability properties are investigated for the case of rectangular electron and ion density profiles. The parameter &dgr;= (2&ohgr;2pe/&ohgr;2ce)   (1−f) is introduced as a convenient measure of the relative strengths of the equilibrium self‐electric force and the magnetic force on an electron fluid element. (Here, &ohgr;⁁peis the electron plasma frequency, &ohgr;ceis the electron cyclotron frequency,f=n0i/n0eis the fractional charge neutralization, and &dgr;=1 corresponds to the maximum allowed charge density for radial confinement of the equilibrium configuration.) An important conclusion of this study is that the equilibrium self‐electric field can have a large influence on stability behavior. In particular, stability properties for &dgr;≲1 differ substantially from those obtained when &dgr;≪1. Moreover, for nonneutral plasma column with significant charge neutralization, it is found that the fundamental mode (l=1) is not the most unstable mode. Rather, higher harmonic perturbations have larger growth rates. However, in the limiting case wheref≪1 and &dgr;≪1, thel=1 mode can have the largest growth rate, which is consistent with the result previously obtained by Levy, Daugherty, and Buneman.