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The starting conditions for excitation of backward waves in the beam tunnel between an electron gun and a cavity of a high-power gyrotron are studied. The excitation of these waves leads to electron energy spread that spoils the beam quality and, hence, degrades the gyrotron efficiency. The suppression of these modes by a resistive coating on the wall of a smooth beam tunnel is examined. The guiding magnetic field and the tunnel wall radius vary along the axis, and thus, the theory is essentially the small-signal theory of a gyro-backward-wave oscillator (gyro-BWO) with tapered parameters. The results obtained are applied to a sample gyrotron.