A class of nonreciprocal bianisotropic media, known to allow a decomposition of electromagnetic fields into two individual parts with certain restrictions on polarization defined in terms of two arbitrary vectors, is studied. The field decomposition principle is extended to electromagnetic sources. It is shown that the medium in the two partial problems can be replaced by simpler equivalent media and that an analytic Green dyadic expression can be formulated for each of the two equivalent media filling the whole space. Thus the decomposition makes it possible to find the field of an elementary source in the original medium by integrating the field of the partial sources. ¿ 1999 American Geophysical Union