Certain classes of ionic solids exhibit ionic conductivities, at temperatures appreciably below the melting point, which are comparable with those found in liquid electrolytes (these compounds are sometimes referred to as fast-ion conductors or superionics). Fluorites represent one such class which possess a relatively simple structure. In these materials the high ionic conductivity is due to disorder in the anion sublattice. A rather diffuse specific heat anomaly related to the disorder occurs at a temperature Tc. The aim of the present study is to provide information about the nature of this dynamic disorder using neutron-scattering techniques. Attention has been focussed on PbF2, SrCl2 and BaF2 which have values of Tc ≈ 830, 1 000 and 1235 K respectively. Certain Bragg reflections show marked variation with temperature in the vicinity of Tc and anomalies have also been observed in the energies, widths and intensities of individual phonons. The origins of these anomalies are discussed