Analysis of X-ray absorption fine structure spectra of UO(2+x) for x = 0-0.20 (UO(2)--U(4)O(9)) reveals that the adventitious O atoms are incorporated as oxo groups with U--O distances of 1.74 A, most likely associated with U(VI), that occur in clusters so that the UO(2) fraction of the material largely remains intact. In addition to the formation of some additional longer U--O bonds, the U sublattice consists of an ordered portion that displays the original U--U distance and a spectroscopically silent, glassy part. This is very different from previous models derived from neutron diffraction that maintained long U--O distances and high U--O coordination numbers. UO(2+x) also differs from PuO(2+x) in its substantially shorter An-oxo distances and no sign of stable coordination with H(2)O and its hydrolysis products.