A set of quasielastic neutron scattering experiments on solid solutions of sodium orthophosphate and sodium sulfate is reported. These materials are not only fast-ion conductors in their high-temperature cubic phases but also show considerable dynamic reorientation disorder of their tetrahedral anions. High resolution backscattering experiments were used to examine sodium diffusion in xNa(2)SO(4) . (1-x)Na3PO4, which was found to be dominated by thermally activated jumps between tetrahedrally coordinated sites, the activation energies ranging from 0.64 eV for x=0.0 to 0.30 eV for x=0.5. Time-of-flight scattering proved to be mainly sensitive to oxygen scattering and thus to anion reorientation. This thermally activated motion exhibits activation energies between 0.184 eV (x=0.0) and 0.052 eV (x=0.5). Analysis of the quasielastic intensities as a function of scattering vector Q gives clear evidence of the involvement of cations in the anion motion. (C) 2004 Elsevier B.V. All rights reserved.