Laser diodes subject to a delayed optical feedback may exhibit high-frequency oscillating intensities as a result of a beating between two external-cavity-modes ͑ECMs͒. We analyze the conditions for the stability of these microwave oscillations in the framework of the Lang-Kobayashi equations for a single-mode edgeemitting semiconductor laser ͓R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 ͑1980͔͒. We show that two different scenarios are possible. If the linewidth enhancement factor is relatively large (␣ϭ2 Ϫ5), the beating occurs between a stable ECM ͑mode͒ and an unstable ECM ͑antimode͒. The stability of the time-periodic solution is then limited in parameter space. But if the linewidth enhancement factor is sufficiently low (␣р␣ c Ӎ1), a beating between two stable modes is possible allowing stable high-frequency oscillating outputs
