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In this paper, the surface waves excited at the edge of a wedge characterized by anisotropic impedance faces are analyzed, when the edge is illuminated by an arbitrarily polarized plane wave at oblique incidence. In the wedge scattering problem, these guided wave modes are associated with pole singularities exhibited by the angular spectra for the total field in the region surrounding the wedge. The location of the above pole singularities determines the wave vector and the existence region of the corresponding SW, while their complex amplitude is provided by the pole residue. A general equation for the SW wave vectors is derived that is valid for any surface impedance tensor and independent of the geometrical wedge configuration.