A finite-difference frequency-domain (FD-FD) formulation is developed to study the dispersion characteristics of anisotropic dielectric waveguides with their optical axes not aligned with the coordinate-system axes. In this analysis, the optical axes are initially assumed to be aligned with the coordinate-system axes such that the electric-permittivity and magnetic-permeability tensors are diagonal. The optical axes of the anisotropic dielectric are then rotated an angle theta (or phi) with respect to the coordinate-system axes, While the FD-FD formulation developed is general, it is applied here only to waveguides containing uniaxial anisotropic dielectrics. The results show that accurate optical-axis orientation is important in the design of dielectric waveguides.4510117891792