We present the quasi-analytical spatiotemporal theory, which describes the process of establishing generation in a backward-wave gyro-oscillator based on the use of a sectioned quasi-optical system with the zigzag path of the operating wave beam. This theory explains peculiarities (namely, a piecewise character) of changing the operating frequency and power of the output signal in the process of the broadband frequency tuning provided by changing the operating magnetic field. This theory also describes competition of different modes of the system in the process of excitation of auto-oscillators and predicts the possibility for realization of the regime of automodulations of the output power, as well as the regime of formation of a short powerful super-radiant pulse.

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