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This paper addresses the problem of evaluating the mutual coupling between slots cut in arbitrary cylindrical structures. The analysis of fields radiated in the exterior region of such a structure requires a numerical evaluation since there exists no analytical Green's function for the general three-dimensional (3-D) problem. The 3-D problem is reduced to a number of two-dimensional (2-D) problems by performing Fourier transform of fields and sources with respect to the axial (z) direction. The 2-D problems are formulated in terms of integral equations in kz (wave number in the z direction) space, and they are solved by the moment method. Mutual coupling expressions for slots cut in rectangular waveguide walls are obtained from an inverse Fourier transform of the 2-D spectral domain solutions. Comparisons to similar analyses in the prior literature for self-admittance of isolated slots and mutual admittance between pairs of slots are made. Efficient methods of determining the spectral domain solutions, criteria for sampling and truncation of the spectrum, and some representative results are presented.