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Analytic expressions of electromagnetic fields for the dominant hybrid-mode in a twisted rectangular waveguide are obtained. The fields exactly satisfy the boundary conditions on the guide walls in a helicoidal shape. By expanding these expressions for the fields in terms of the eigenfunctions of a straight waveguide, the hybrid-mode is found to be composed of a fundamental TE10 -mode component, accompanied with TE01, TM21,TE21, and TE03 modes, as successive higher order components. The result of the modal power calculation reveals that there exists a frequency at which the transmitting power carried in the cross-polarized TE01-mode component just vanishes. As a limiting case of the twisted waveguide, fields in a twisted strip line are discussed also, and the existence of a propeller-like equiphase surface is shown.