Loss-guided optical waveguides have propagation operators which are linear but not self-adjoint. The eigenmodes of such nonHermitian systems are then not orthogonal but rather are biorthogonal to a set of adjoint functions. If one wishes to expand an arbitrary wave in the eigenmodes of the system, it is tempting to find the expansion coefficients using the biorthogonality relation to obtain quadrature integrals between the propagating wave and the adjoint functions. We show however that a minimum least-square error expansion is obtained not by using these adjoint integrals, but by a more complex procedure based on inverting the eigenmode orthogonality matrix. For the particular case of Hermite-Gaussian functions having a complex-valued scale factor, expansions using the adjoint coefficients fail to converge under a wide range of circumstances, whereas the minimum-error coefficients converge and give much smaller errors under all circumstances.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.