The structures of ices III and V have been studied under their thermodynamic conditions of stability by neutron diffraction. The results clearly indicate partial ordering of the water molecule orientations for both ice structures. For ice V the ordering is both pressure and temperature dependent, while no significant changes in ordering were noted for ice III within the small region of stability. No reduction in symmetry, necessary for complete orientational ordering, was observed for ice V at low temperatures. The ordering behavior of ice V at low temperatures (< 150 K), when considered in conjunction with dielectric measurements at high temperatures, suggests that while relaxation is achieved predominantly through the diffusion of rotational defects at high temperatures, the mechanism at low temperatures appears to be the migration of ionic defects which require only a small activation energy for mobilization. (C) 2000 American Institute of Physics. [S0021-9606(00)51715-2].