The evolution of rf-accelerator technology toward high-power, high-current, lowemittance beams produces an ever-increasing demand for efficient, very high power microwave power sources. The present klystron technology has performed very well but is not expected to produce reliable gigawatt peak-power units in the 1- to 10-GHz regime. Further major advancements must involve other types of sources. The reflexing-electron class of sources can produce microwave powers at the gigawatt level and has demonstrated operation from 800-MHz to 40-GHz. The pulse length appears to be limited by diode closure, and reflexing-electron devices have been operated in a repetitively pulsed mode. A design is presented for a reflexing electron microwave amplifier that is frequency and phase locked. In this design, the generated microwave power can be efficiently coupled to one or several accelerator loads. Frequency and phase-locking capability may permit parallel-source operation for higher power. The low-frequency (500-MHz to 10-GHz) operation at very high power required by present and proposed microwave particle accelerators makes an amplifier, based on reflexing electron phenomena, a candidate for the development of new accelerator power sources.