Based on a nonlinear, local mode–mode coupling relation, the resonant interaction of flute‐interchange modes with radio frequency (rf ) wave fields in the ion‐cyclotron range of frequencies (ICRF) is studied. It is shown that interchange modes can be stabilized because of resonant coupling to electrostatic ion‐cyclotron sidebands. Stabilization takes place if the frequency of the rf field is somewhat higher than the local ion‐cyclotron frequency, as observed in contemporary experiments on mirror devices.