Abstract The cutoff wavenumbers k nm and the field of surface wave modes of a circular cylindrical conductor eccentrically coated by a dielectric are determined analytically. The electromagnetic field is expressed in terms of circular cylindrical wave functions referred to both axes, in combination with related addition theorems. When the solutions are specialized to small eccentricities kd, where d is the distance between the two axes, exact closed-form expressions are obtained for the coefficients g nm in the resulting relation k nm(d)=k nm(0)[1+g nm(k nmd) 2+...] for the cutoff wavenumbers of the waveguide. Similar expressions are obtained for the field. Numerical results for all types of modes are given. For certain values of the parameters, it is possible to enhance the operating bandwidth of the basic hybrid mode HE 11 over the conventional concentric guide.