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Efficient second-harmonic power extraction was demonstrated recently with GaAs TUNNETT diodes up to 235 GHz and with InP Gunn devices up to 325 GHz. This paper discusses the latest theoretical and experimental results from second-harmonic power extraction at submillimeter-wave frequencies and explores the potential of using power extraction at higher harmonic frequencies to generate continuous-wave radiation with significant output power levels at frequencies above 325 GHz. Initial experimental results are more than 50 μW at 356 GHz from a GaAs TUNNETT diode in a third-harmonic mode and at least 0.2-5 μW in the frequency range 400-560 GHz from InP Gunn devices in a third or higher harmonic mode. The spectral output of these submillimeter-wave sources was analyzed with a simple Fourier-transform terahertz spectrometer and, up to 415 GHz, with a spectrum analyzer and appropriate harmonic mixers.