A recently introduced system of partial differential equations, based on physical considerations, which describes the behavior of electro-magnetic waves in artificial absorbing layers, is analyzed. Analytic solutions are found, for the cases of semi-infinite layers and finite depth layers, both for primitive and characteristic boundary conditions. A different set of equations that seem to offer some advantages is proposed in this paper. The properties of its solutions for the same geometries and boundary condition are also discussed, (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.