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A quasi-optical gyrotron can operate, in principle, at high harmonics of the electron-cyclotron frequency, as well as at the fundamental. Lower harmonics are suppressed by exploiting their larger diffraction losses. The radiation-field amplitude is kept below the breakdown value by taking advantage of the focusing properties of the quasi-optical resonator. Cavity design parameters and starting currents are presented which characterize the operation of the quasi-optical gyrotron at the eighth harmonic of gyrofrequency.