The dispersion characteristics and slow-wave instabilities of a sinusoidally corrugated waveguide with coaxial slow-wave structure (SWS) are analyzed. In SWS, a central cylindrical conductor is surrounded by an outer cylindrical conductor. Sinusoidal corrugation is formed on either conductor or both conductors. The corrugation parameters are those used for an X-band SWS. The relative phase between the sinusoidal corrugations on the inner and outer conductors affects the dispersion characteristics. Instabilities due to beam interactions with the slow -waves are examined by considering three-dimensional beam perturbations. The slow cyclotron instability occurs in addition to the Cherenkov instability, since transverse as well as longitudinal perturbations are included.