The high-temperature cubic phases of sodium hydroxide and potassium hydroxide have been investigated using X-ray, elastic and inelastic neutron scattering from single crystals. As a special feature of these experiments the crystals had to be kept at temperatures of around 550 K as grown from melt, since they are destroyed when passing through the structural phase transition. In these compounds the OH or OD groups are known to undergo rapid reorientational motions. The X-ray diffraction results are characterized by a rapid decrease in the Bragg intensities with increasing diffraction angle and diffuse rods passing through the Bragg reflections. By neutron diffraction, about 20 symmetrically non-equivalent reflections have been observed. Different means of analysis will be presented; one obtains the probability distribution of H+ or D+ around oxygen, and the OH distance. This is of interest in the context of possible H bonding and proton conductivity. The disorder of H or D gives rise to diffuse scattering of neutrons as an approximately spherical halo around the origin in Q-space. The orientations of OH groups at different sites being correlated cannot be excluded from the experimental findings; a 2D correlation model, however, does not predict a dramatic narrowing of this halo. Inelastic scattering yielded rather ill-defined phonon groups in constant-Q scans. In particular, the shear modes showed strong overdamping. The observed features can be explained by treating the OH groups as elastic dipoles coupled to the lattice distortions, with the dynamics of a relaxator, and by extending conventional soft-mode theory to allow for the mixing of several softened modes. The softened modes also explain the diffuse rods in X-ray photographs.