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We study theoretically the processes which take place in a relativistic backward-wave oscillator (BWO) in the parameter region corresponding to hard excitation of oscillations. The onset of both stationary oscillations near the boundary of the hard excitation regime and hard nonstationary oscillations realizing the self-modulation regimes of BWO operation are analyzed along with the dynamics of a BWO-based amplifier. In particular, it is shown that hard excitation of selfoscillation can restrict significantly the output characteristics of a relativistic BWO operated in the regenerative-amplification regime.