This paper presents a full-wave hybrid approach to analyze complex (lossy) dielectric open waveguides. The configuration consists of inhomogeneous and homogeneous regions and is bounded by open space. The inhomogeneous regions are analyzed by a finite element method and the homogeneous ones by a boundary integral equation technique. The presented method makes efficient use of the matrix sparsity originating from the finite elements. The technique is applied to obtain the dispersion characteristics and eigenfield patterns of modes propagating in anisotropic waveguides. ¿ American Geophysical Union 1996