Complex waves in shielded lossless inhomogeneous waveguiding structures are investigated. A new theoretical approach for wave interaction, which may result in complex modes, is developed using the theory of coupled modes. It is shown that complex modes may exist in perturbed homogeneous waveguiding structures as a result of the coupling of a pair of degenerate or nearly degenerate modes. Coupled modes, in microstrips and fin lines, are discussed and numerical data are compared.