Conditions are determined for the stability of two identical colliding ion beams in the presence of neutralizing electrons, but no background ions. Such a situation is envisioned for the Counterstreaming Ion Torus. The ion beams are taken to be Maxwellian in their frames of reference. The approximation of decoupled electrostatic and electromagnetic modes is made. The stability of the electrostatic modes depends on the relation between the ion‐electron temperature ratio and the relative beam velocities. The stability of the electromagnetic mode depends on the relation between the ion plasma &bgr; and the relative beam velocities.