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Theoretical analysis and numerical results of the dispersion characteristic of a periodic circular waveguide loaded by an azimuthally magnetized ferrite rod are presented. Higher order modes are included in the slot region such that circularly non-symmetric quasi-TE modes that are affected by the corrugations can propagate. The space harmonics in the ferrite-rod are expressed in terms of special functions given by series expansions and asymptotic expressions. The boundary value problem is solved by truncating the infinite order determinantal secular equation at some highest order. Dispersion curves for quasi-TE (HE) and quasi-TM (EH) modes are given.