In an effort to formulate the high-frequency coupling between antennas located on airframes composed of multilayer imperfectly conducting materials a general model was sought which would embody the electromagnetic properties of the layers and would apply over a broader range of separations of the antennas. Such a model is described here. This work is a generalization of the work of Pearson <1986, 1987a> concerning the high-frequency asymptotic representation of the fields of elemental sources diffracted by a multilayer cylinder. In that work the source and field points were located off the cylinder surface, and they were sufficiently separated to permit the effective use of the residue series representation of the spectral integrals involved. Here the source and field points are located on the cylinder surface and are permitted to be sufficiently close as to render the residue series poorly convergent. To obtain a more effective representation in this situation, the cylinder is modeled by an anisotropic impedance cylinder, and the resulting spectral integrals are evaluated by reduction to forms amenable to multiple applications of techniques described in the literature in connection with treatment of axially uniform sources in this context. ¿ American Geophysical Union 1996