The atomic structure of amorphous Tb20Fe80 thin films has been studied by Extended X-ray Absorption Fine Structure (EXAFS) of both Fe K and Tb LIII absorption edges. The local site geometry around Fe atoms shows predominantly Fe nearest neighbors with an Fe-Fe distance distribution centered on 2.50±0.02 Å and a coordination number of 9.1±1. In contrast, the radial structure function (RSF) obtained at the Tb edge is broad and asymmetric. The peak in the RSF corresponds to a Tb-Fe near neighbor distance of 2.94±0.1 Å with no evidence for Tb-Tb nearest neighbor coordination. The width and the shape of the RSF suggest that the Tb-Fe atomic environment is anisotropic and strained probably as a consequence of the growth process. This distorted atomic environment is suggested to be responsible for the magnetic anisotropy in these alloys. Thermal annealing at 200 °C leads to reduction in Ku. We propose that this results from reordering of the Tb local environment such that the average structural anisotropy in the distribution is reduced. EXAFS data show that annealing at 400°C causes precipitation of bcc polycrystalline Fe. The addition of 7 at.% Au to the alloy prevents this recrystallization and preserves the amorphous state but does not prevent the structural relaxation which reduces Ku at lower temperatures. © 1989 Springer-Verlag.