The stability of a charge and current neutralized electron‐ion beam propagating between two planar boundaries is investigated. For equipotential boundaries the beam is, as originally shown by Pierce, electrostatically unstable for electron current densities above a certain limiting value. If, however, the electric field at the upstream boundary is required to vanish, there is no instability. An intermediate case, in which the two boundaries are electrically connected with a finite conductivity plasma, corresponds to the proposed use of neutralized light and heavy ion beams for inertial confinement fusion drivers. Results indicate such beams can propagate either stably or with zero‐frequency Pierce instability growth rates which are probably insignificant. lectric currents; boundary conditions; current density; electric fields; plasma;