Circular magnetic x-ray dichroism (CMXD) has been used to probe the magnetic properties of rare earth compounds. This study has been undertaken in two distinct parts. First, the angular dependence of the CMXD signal has been examined in order to determine the multiple nature of the transitions involved. Second, the nature of the dichroic spectra of amorphous and crystalline GdFe[subscript]2 has been probed. CMXD offers a unique probe of the magnetic properties of amorphous materials providing information that is not available from any other technique;Previous CMXD measurements at the L edges of rare earth materials have demonstrated two distinct features, one above and one below the Fermi energy. Theoretical calculations have ascribed the two features to dipolar and quadrupolar transitions to the empty 5d and 4f states respectively. This study sought to determine the multipole nature of the transitions involved by measuring the angular dependence of the CMXD signal. Two experiments attempting to observe this angular dependence were undertaken, one at the L[subscript]3 edge of Er in Er[subscript]2Fe[subscript]14B, and another at the L[subscript]2 and L[subscript]3 edges of grain oriented REFe[subscript]2 compounds. All features in the CMXD spectra, within experimental error, were found to be consistent with dipolar transitions. We discuss some possible reasons for the apparent absence of the predicted quadrupolar angular dependence of the features below E[subscript] f.;The spin dependent absorption of circularly polarized x-rays at the K edge of Fe and the L[subscript]2 and L[subscript]3 edges Gd in amorphous and crystalline GdFe[subscript]2 has also been studied. Large differences in the magnitude of the dichroic signal are observed between the two samples. The application of recently derived sum rules indicated substantial quenching of the orbital moment in the amorphous sample. The results are compared to a theoretical spectrum for crystalline GdFe[subscript]2.