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The eigenmodes of the empty toroidal cavity, relevant for H. F. heating of toroidal plasmas, are calculated using a development in the inverse aspect ratio. The eigensolutions are classified as quasi-TE and quasi-TH modes according to their cylindrical limit. Two exceptional modes are found for which both the electric and the magnetic field in the axial direction are nonzero already to the lowest order. The existence of these modes is connected with the accidental degeneracy of the cylindrical TH1 and TE0 modes.