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In this paper, a novel full-wave method for the modal characterization of periodic structures loaded with elliptical waveguides is presented. This method relies on an integral equation formulation solved via the method of moments, which finally leads to the solution of a standard eigenvalue problem. The required modal spectrum of elliptical waveguides is determined through the boundary integral-resonant mode expansion technique. For validation purposes, the proposed analysis method is first successfully applied to periodic waveguide structures already considered in the technical literature. Then, our new algorithm is used to compute the related Brillouin diagrams and the interaction impedance of new periodic structures loaded with elliptical waveguides. Not only the main interacting mode (such as the TM 01 mode) is studied, but higher-order Floquet modes are also considered. These results have potential applications as slow-wave structures for high-power microwave devices and possibly filtering structures at millimeter-wave frequencies.