The stability of circular waveguide modes perturbed by a relativistic electron beam is investigated. The electron beam propagates along the waveguide and is guided by an applied uniform axial magnetic field. The electron beam is represented by a distribution of rigid rotators all having the same energy and Larmor radiusrLwith their guiding centers centered on a circle or radiusRbaround the guide axis. Numerical results are presented giving a general view of the competition between synchronous and cyclotron instabilities for TM and TE modes as a function ofrLandRb.