In this paper a generalized theory of coupled local normal modes is developed, which is based on the mathematical method-"method of slowly varying coefficients", introduced by the author in a previous paper. By this method, the set of ordinary coupled wave equations is transformed into a new set of equations for the local normal modes with much reduced couplings. To illustrate the applicability of the method, the all-important problem of bend with slowly varying curvature is solved by considering two and three coupled modes succesively. For the two coupled-modes case, our results agree with those by Louisell and Unger. Solution for the three coupled-modes problem has not been appeared in literatures heretofore. A numerical evaluation of the spurious modes in an S-shaped bend is given. Further applications are discussed.