The local structures around rare-earth ions in rare-earth ultraphosphate glasses (nominally 15RE2O3-85P2O5, mol%, RE = Nd, Sm, Gd, Ho, and Er) and metaphosphate glasses (nominally 25RE2O3-75P2O5, mol%, RE = Nd, Gd, and Er) have been studied by extended X-ray absorption fine structure spectroscopy (EXAFS) at the respective rare-earth LIII edges. The RE-O distance decreases with increasing atomic number of the rare-earth ion for both ultra and metaphosphate glasses. On average, RE-O distances for metaphosphate glasses are shorter than those for ultraphosphate glasses of comparable compositions. There are 7-8 oxygen nearest neighbors in the first co-ordination sphere around rare-earth ions in ultraphosphate glasses and not, vert, similar6 oxygens in the first co-ordination sphere around rare-earth ions in metaphosphate glasses. There is no systematic dependence of the RE-O co-ordination number on the atomic number of the rare-earth ions in either compositional series. The second co-ordination shell around rare-earth ions in ultraphosphate glasses consists of phosphorus ions for all but the samarium ultraphosphate glass, with a RE-P distance between 3.53 and 3.85 Å and co-ordination numbers between 3 and 5. No RE-RE correlations were found within a distance of 4.5 Å.