Expressions are derived for the initial relaxation rate 1/ T 1 of protons and deuterons of nontunnelling NH 4 and ND 4 groups reorienting about various symmetry axes in solids. The reorientation rates are modified by a trigonal, tetragonal or monoclinic distortion of the predominantly cubic hindering potential. When the rates differ sufficiently from each other, two T 1 minima are observed with a characteristic ratio. Experiments were performed in NH 4VO 3, (NH 4) 2S 2O 8, (NH 4) 2PtCl 4, and their deuterated modifications, which all exhibit two T 1 minima. In NH 4VO 3 and ND 4VO 3 the relaxation and spectral data agree rather well with the model of trigonal distortion. Also (NH 4) 2S 2O 8 has a preferred threefold axis but there, the large tunnel splitting of protons has to be taken into account before an agreement is reached. All the purely reorientational models fail with (NH 4) 2PtCl 4, where, instead, the ammonium groups are proposed to be ordered into domains at low temperatures. The groups inside the domains and boundary regions give rise to the high- and low-temperature T 1 minima, respectively. The boundaries are also believed to give rise to the narrow component in the deuteron spectrum at low temperatures. Evidence for a proton tunnelling frequency of 32 MHz is found in (NH 4) 2PtCl 4.