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A solution is presented for the mutual coupling between the modes of different-sized circular coaxial aperture arrays, which are used as direct radiators and feed antennas. This solution is expressed in terms of integral transforms and the mutual admittances for the cross coupling between all three mode types, TE, TM, and TEM, are obtained. The accuracy of this new integral formulation is demonstrated by comparing computed results with measured data for a three-element test array. Excellent agreement is obtained between theory and experiment for both coupling coefficients and radiation patterns. Results are also presented for a coaxial feed array for the Lovell radio telescope.