Cherenkov and slow cyclotron instabilities driven by an axially injected electron beam in periodically corrugated cylindrical waveguide are studied by using a new version of self-consistent linear theory considering three dimensional beam perturbations. For the bounded microwave systems, the self-consistent boundary conditions require all field components and the normal modes in the beam are hybrid of transverse magnetic (TM) and transverse electric (TE) modes, even in the axisymmetric case. The slow cyclotron instability as well as Cherenkov instability can be driven by the axially streaming electron beam without any initial perpendicular velocity. In the low magnetic field region, the charge caused by the radial displacement of the beam plays an important role in the beam interaction with the electromagnetic mode. The radial displacement become large by decreasing the magnetic field and the slow cyclotron instability becomes strong and compete with the Cherenkov instability. For the axisymmetric case, the Cherenkov instability is dominant and suppresses the slow cyclotron instability, On the other hand, the slow cyclotron instability becomes dominant and suppresses the Cherenkov instability, for the nonaxisymmetric mode with the left-hand circular polarization. © 2004, The Institute of Electrical Engineers of Japan. All rights reserved.