The fluorine nuclear magnetic resonance spectra of the sodium, potassium, rubidium, and cesium hexafluorophosphates were studied between 77° and 400°K. It was found that in each of the salts the PF6—ions are reorienting about the octahedral axes at random, or nearly so, for temperatures of 200°K and above. The broadening of the fluorine resonance in these solids at lower temperatures indicates that the ease with which the PF6— groups reorient increases with increasing size of the alkali metal cation, so that for CsPF6 the fluorine resonance is still narrow at 77°K. A quantitative study of the potential barriers to PF6— group reorientation was discouraged by the discovery that the fluorine line shapes and linewidths are remarkably sensitive to the physical state and, in the case of RbPF6, the thermal history of the sample. These effects are attributed to crystal imperfections which lower the potential barriers to PF6— group reorientations and decrease the size of domains in which there is a cooperative ``freezing out'' of the reorientations. Thus, in the region of changing linewidth, we postulate domains with frozen-out PF6— groups and others with reorienting groups. In samples which should have relatively low imperfection concentrations and where such domains should be large, we find distinguishable broad and narrow components in the fluorine resonance, with one growing at the expense of the other as the temperature is changed. This two-phase behavior disappears in finely powdered samples, in which high concentrations of imperfections were probably introduced by the mechanical grinding. Fluorine line-shape studies reported previously for solid CF4 are reinterpreted in terms of a similar two-phase, cooperative process for the freezing out of the CF4 reorientations.