Some designs for tandem mirror devices rely on a thermal‐barrier cell, a region of depressed potential located between the central cell and the end plugs. This region of depressed potential relies on, to some extent, an ion distribution function that has two peaks invz(ion velocity parallel to the magnetic axis). Therefore there is a possibility that some ion–ion two‐stream modes can be unstable. Using one‐dimensional models, the stability of model equilibria to electrostatic ion two‐stream modes is considered. The results suggest that for parameters of greatest interest (i.e., for planned experiments), these modes could be stable. Particle simulation techniques are used to examine the nonlinear consequences for those conditions where instability is present.