The Van Kranendonk theory of quadrupolar nuclear spin–lattice relaxation is adapted to the case of the X nuclei in R2MX6 compounds as observed in a pure nuclear quadrupole resonance experiment. The formula derived for the spin–lattice relaxation time is discussed with reference to experimental data for three R2PtCl6 compounds. The internal modes of the PtCl6 complex are shown to be relatively unimportant for spin–lattice relaxation of the chlorine nuclei. The experimental data yield average rotary mode frequencies of the PtCl6 complex in K2PtCl6, Rb2PtCl6, and Cs2PtCl6. The results are in good agreement with the theoretical predictions.