Recent and novel data obtained from chlorine NQR measurements on natural and deuterated (NH4)2MCl6 compounds are discussed with special regard to the influence of the ammonium-ion dynamics on the structural stability of these crystals. The temperature dependence (4.2 K to 350 K) of the chlorine NOR frequency vQ and relaxation rates T1-1 , T2-1 obtained from the natural ammonium salts of Sn, Pd, Os, Pb, Te, Se and from the deuterated salts of Sn, Te and Se are analysed. Slight deviations from the normal temperature behaviour of vQ and T1-1 are found in Sn, Pd and Os compounds which stay cubic in the whole temperature range. The ammonium compounds of Pb and Te undergo a structural transformation between 80 K and 90 K from the cubic to a trigonal phase which is distinguished by the preservation of the single line spectrum of the chlorine NQR below rel. The observed divergence of T1-1 at the transition point can be described in terms of a spin-phonon process in the presence of an overdamped soft mode. Deuteration of (NH4)2TeCl6 only slightly affects the transition of Tc2 but leads to new structural changes at lower temperatures. Whereas the natural compound stays trigonal down to 4.2 K the deuterated crystal undergoes two additional structural transformations at Tc2 = 48 K and Tc3 = 28 K which are correlated with a slowing down of the deuteron motion. Approaching Tc2 from above, the spin-lattice relaxation rate and the spin-spin relaxation rate of the chlorine NQR exhibit distinct anomalies which are attributed to limited jumps of the octahedron in a shallow potential. The barrier height of this potential deduced from the chlorine NQR spin-lattice relaxation rate is 400 K. The transition at Tc2 is explained by the condensation in one minimum of this potential. At Tc3 a long range correlation is formed which is accompanied by a rotation of the octahedron about its fourfold axis. A similar mechanism is adopted for the transitions observed in (NH4)2SeCl6 at Tc= 24 K and in (ND4)2 SeCl6 at Tc = 48 K.