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An order-reduced volume-integral equation approach is proposed for modeling and analyzing of nonradiative dielectric (NRD)-guide and H-guide millimeter-wave circuits that involve arbitrarily shaped planar geometry and inhomogeneous dielectric. A half-sinusoidal vertical variation of fields is used so that the discretization of current for the volume-integral equation is made in the parallel plane. Combined basis functions of propagating and local modes are used in the Galerkin's method of moments on the basis of spectrum analysis of the NRD-guide and H-guide. A vertical integration in the space domain is carried out analytically and a first-order Green's function with m=1 is developed. The solution for the volume-integral equation in modeling NRD-guide and H-guide circuits is then reduced to a two-dimensional planar problem. This technique can be applied for calculating the characteristics of various waveguide components and multiport circuits such as resonant frequencies and S-parameters. The framework of this technique is demonstrated through its application to an NRD-guide open-end. In addition, an H-guide open-end, three types of resonators, and three-pole gap-coupled NRD-guide filters are modeled and analyzed. The results are in good agreement with the measurements and results obtained by other methods.