Wave propagation in optical waveguides deposited on gyrotropic and anisotropic substrates is analyzed in terms of the eigenmodes of the guide. The field composition and the phase velocity of the eigenmodes are determined. The results of the analysis are applied to waveguide modulators and distributed‐feedback lasers for use in integrated optics. Based on the eigenmode analysis, coupled‐wave equations are set up to facilitate the analysis of integrated‐optics problems which involve the use of gyrotropic and anisotropic waveguides.