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In two recent papers , , Oughstun et al. have claimed that the eigenvalues of the transverse modes traveling along opposite directions in ring cavities are different. Using very general arguments based on the symmetry of the free-space kernel, we show that the two sets of eigenvalues associated with the counterpropagating modes of ring cavities are formally identical. The two sets of counter-propagating eigenfunctions satisfy a biorthogonality relationship.