The dynamics of the ZnCl₄ anion in two compounds, one exhibiting a structural transition to an incommensurate phase (Rb₂ZnCl₄) and another not having any structural transition at all (Cs₂ZnCl₄), are studied through ³⁵Cl NQR frequency ( nu ) and relaxation time (T_1Q) measurements as a function of temperature T in their high-temperature (paraelectric) phases. Estimates of the potential barriers hindering the reorientational motions of ZnCl₄ anions along axes parallel and perpendicular to the a axis of the crystal structure are obtained from the T_1Q data. These results are analysed in conjunction with a qualitative comparison of relative mean square amplitudes of such motions obtainable from frequency data, in order to investigate the differences in the dynamics and structure of the ZnCl₄ anion. There seems to be correlation between the dynamics of the anion in this phase and the possibility that the compound may exhibit a structural instability at low temperatures in this family.