The Beckmann and Clough theory (see ibid., vol.10, p.L231 (1977)) of proton spin-lattice relaxation due to coupling of lattice vibrations with rotational motion of methyl groups is extended to the case of ammonium ions. It is found that the effect may be dependent on magnitudes of tunnelling and Zeeman splittings. For ammonium perchlorate the activation energy obtained from T₁ measurements is demonstrated to be approximately equal to the position of the optical phonon peak in the lattice spectrum in agreement with the theoretical prediction.