Azimuthal surface waves are eigenmodes of cylindrical plasma–dielectric–metal structures both in the presence of and without an axial static magnetic field. They are actively studied due to possible applications in plasma electronics, nanotechnologies and biomedical diagnostics. Higher radial modes are known to propagate at higher frequencies and shorter wavelengths compared to those of the zeroth mode, a feature which is of interest for practical applications. To gain the advantage of the excitation of higher radial modes of azimuthal surface waves one has first to know their dispersion properties. This paper generalizes the results of earlier papers by including a static axial magnetic field and considering the higher radial modes. The presence of the constant axial magnetic field removes the degeneracy in the wave spectrum with respect to the sign of the azimuthal wavenumber.