A detailed study of the x-ray magnetic scattering from Tb has been performed, including polarization analysis of the scattered intensity as a function of energy close to the and absorption edges. Large enhancements of the magnetic signal are observed at these energies. It is found that the enhancement at the edge is consistent with a simple dipole transition model, whereas the enhancement at the edge shows an anomalous splitting. The angular and polarization dependences of this resonance are investigated, and various explanations are discussed.