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Electromagnetic wave propagation in a coaxial elliptical transmission line is investigated theoretically, the medium filling the space between the elliptical cylinders being a longitudinally magnetized plasma. Assuming an imperfect inner conductor throughout the treatment, exact numerical values for the complex propagation constant are determined through a special algorithmic process. Dispersion diagrams are given for propagation in weakly and strongly ionized media for several geometrical configurations of the structure. The influence of collisions in the values of propagation constant is also investigated. Conclusions are drawn for the possibility of propagation of the modes based on the size of the determined attenuation constant.