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The electromagnetic scattering from partially or totally penetrable bodies of revolution (BOR) is formulated in terms of coupled Fredholm integral equations, solved by the method of moments (MM). The scatterers can have axial inhomogeneities, formed by dissimilar dielectric materials. The case of conducting bodies with axially discontinuous coatings is also treated. The penetrable regions can be lossy, characterized by complex permeability and permittivity. Boundary conditions are rigorously treated everywhere including the intersection of the various regions. The solutions are expressed in terms of combinations of two special matrices arising from the Galerkin technique. These solutions are implemented numerically for a class of generic axially inhomogeneous BOR scatterers. Numerical results given for various conducting/dielectric cylinder combinations using this formulation are compared with experimental data. For special cases where comparisons are possible, the present analysis replicates the results of the Mie theory.