The stability properties of coupled dipole resonance oscillations in a relativistic electron‐beam–plasma system are investigated within the framework of a rigid beam model. The analysis is carried out assuming sharp‐boundary rectangular density profiles, and distinguishing the two cases: (a) beam‐electron–plasma‐electron dipole resonance oscillations and (b) the ion resonance instability for an intense relativistic electron beam partially charge neutralized by background ions. In case (a), it is shown that the system is most unstable for zero fractional charge neutralization and that the instability growth rate can be significantly reduced by increasing the density ratio ?e’/?e, where ?e’and ?eare the beam‐electron and plasma‐electron densities, respectively. Moreover, the characteristic growth rate for the electron‐electron dipole resonance instability can be a substantial fraction of the beam‐electron cyclotron frequency. In case (b), it is found that the instability growth rate is enhanced considerably by increasing the beam density and energy and that, for sufficiently small fractional charge neutralization, the most unstable mode occurs for long axial wavelengths (kz=0). The characteristic growth rate for the ion resonance instability is also found to be a substantial fraction of the beam‐electron cyclotron frequency.