Extended X-ray absorption fine structure (EXAFS) has been utilized to investigate the local atomic structure around Th, U, and Pu atoms in polycrystalline mixed dioxides Th(1-x)M(x)O2 (with M = U, Pu) for x ranging from 0 to 1. The composition dependence of the two first-coordination-shell distances was measured throughout the entire composition range for both solid solutions. The first-shell distances vary slightly across the solid-solution composition with values close to those of the pure dioxide parents, indicating a bimodal cation-oxygen distribution. In contrast, the second-shell distance varies strongly with composition, with values close to the weighted amount average distances. Nevertheless, in both systems, the lattice cell parameters, deduced from the first- and second-shell bond determined by EXAFS, are very close to those measured from X-ray diffraction (XRD). They vary linearly with composition, accurately following Vegard's law.