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Two sets of coupled-mode equations for multiwaveguide systems are derived using a generalized reciprocity relation; one set for a lossless system and the other for a general lossy or lossless system. The second set of equations also reduces to those of the first set in the lossless case under the condition that the transverse field components are chosen to be real. Analytical relations between the coupling coefficients are shown and applied to the coupling of mode equations. It is shown analytically that our results satisfy exactly both the reciprocity theorem and power conservation. New orthogonal relations between the supermodes are derived in matrix form with the overlap integrals taken into account.