The transition of the dynamics of ND4+ ions in ammonium persulphate, dominated at low temperatures by coherent uniaxial rotational tunnelling about one specific N-D bond (the preferred bond) and, at high temperatures, by frequent stochastic jumps about all N-D bonds is elucidated with deuteron spin-lattice relaxation measurements, selective saturation experiments and deuteron NMR line shape analyses. Between 20 and 35 K, the coherent uniaxial tunnelling is superseded by thermally activated stochastic jumps about the same bond with kinetic parameters k(dyn)(0)=10((11.5+/-0.5)) s(-1) and E-dyn(a)=(3.6+/-0.3) kJ/mol. At higher temperatures, thermally activated stochastic jumps about the other N-D bonds set in. Their kinetic parameters are k(st)(0)=10((12.2+/-0.5)) s(-1) and E-st(a)=(7.8+/-0.5) kJ/mol. From the primary and secondary tunnelling observed at low temperatures we infer the heights of the potentials which hinder rotations of the ND4+ ions about the preferred and any other N-D bond. These heights, minus the rotator's ground state energy, are about 25% larger than, respectively, E-dyn(a) and E-st(a). The kinetic parameters of the two stochastic processes are such that the essentially uniaxial coherent and then incoherent dynamics at low temperatures is superseded at the decomposition temperature of the compound by stochastic reorientational jumps which reflect the basic tetrahedral symmetry of the ammonium ion.