Linear accelerators driven by pulse forming networks and utilizing beam neutralization may be useful for obtaining high‐current ion beams for inertial fusion applications. Such accelerators may be subject to longitudinal velocity bunching instabilities. These instabilities are studied with a computer simulation of longitudinal ion dynamics. It is found that they are stabilized by a velocity spread in the beam distribution determined by the properties of the pulselines. The required velocity spread does not preclude obtaining beams of sufficient quality for fusion applications.