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The modes of propagation along a coaxial structure contained within a circular tunnel are considered. The primary objective is to develop an approximate impedance boundary condition at the outer surface of the shielded cable that can be used in previously developed formalisms for axial conductors in tunnels. It is assumed that the metal braid can be characterized by a surface-transfer impedance. We also account for the possibility that a Iossy film exists on the outer surface of the dielectric jacket of the cable.