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Using the dielectric tensor for a relativistic electron beam with finite strength axial magnetic field, saddle-point analysis for absolute and convective instabilities in the corrugated metal-wall slow-wave structure of backward-wave oscillators (BWOs) has been carried out. The parameters used in experiments at the University of Maryland were assumed. It is shown that the absolute instability of the BWO ceases, and a convective instability appears instead for a wide range of B near the condition of cyclotron absorption. The experimental results can be explained quantitatively taking into account the effect of finite length of the BWOs.