Deuteron NMR lineshapes are computed for the ND4+ ion, taking into account dipolar and first-order quadrupolar interactions. Expressions for tunnelling-Hamiltonian matrix elements are given as linear combinations of seven overlap integrals related to the symmetry rotations of a tetrahedron. Examples of theoretical lineshapes are presented, exhibiting their sensitivity to tunnelling motions. Tunnelling effects for ND4+ are discussed and compared with related features for NH 4+. From an analysis of experimental lineshapes for ND4PF6 and (ND4)2PtCl6 at 1.6K, tunnelling frequencies of 1.6 MHz and 3.4 MHz respectively, are deduced. In these cases, large volumes of tunnelling splittings suppressed effectively second-order effects in the quadrupolar interaction.