Measurements of the temperature and pressure variation of the 35Cl nuclear spin–lattice relaxation time in Rb2PtCl6 and Cs2PtCl6 are reported. The spin–lattice relaxation time is measured at atmospheric pressure for temperatures from 60 to 500 K and at four temperatures between 290 and 380 K for pressures to 5000 kg cm−2. Previously published data for K2PtCl6 are also included in the discussion. The Van Kranendonk theory of nuclear quadrupolar relaxation forms the basis of the analysis. The rotary lattice mode frequencies are deduced; they are of approximately the same magnitude and increase in the same sequence as the frequencies deduced from nuclear quadrupole resonance frequency measurements and from infrared and Raman data. An analysis of the pressure dependence of the spin–lattice relaxation time data yields order of magnitude pressure coefficients for the rotary mode frequencies. Finally, a thermodynamic analysis, which takes specific volume effects into account by incorporating both the temperature and pressure dependence of the data, is presented.