A spectral domain framework is presented for deriving exact electromagnetic impedance boundary conditions for isotropic, longitudinally inhomogeneous, dielectric coatings on a general (polarization-rotating) impedance plane. The derived expressions are shown to be well approximated over a reasonably wide range of parameters by means of rational functions of the spectral variables, from which higher-order approximate impedance boundary conditions are readily obtained by simple Fourier transformation. The proposed method is readily extended to multilayer coatings consisting of any combination of inhomogeneous dielectric layers and homogeneous, arbitrarily complex (e.g., bianisotropic, nonreciprocal) materials. Application to curved boundaries is also possible. A number of examples are included to validate the proposed approach and show its versatility and reliability. ¿ 2000 American Geophysical Union