We report on a single-crystal deuteron nuclear magnetic resonance (NMR) spectroscopy study of the low-temperature dynamics of ND4+ and NH3D+ ions in the title compound. The most prominent feature of the dynamics of ND4+ ions is uniaxial rotational (primary) tunneling of three deuterons about the N-D bond of the fourth. At T<25 K, the latter deuteron gets localized on the time scale of 10(-3) s. We identify the direction of this unique N-D bond. The low-temperature limit of the primary tunneling frequency is 1.6 MHz. In the form of splittings of NMR resonances, our spectra also contain clear evidence of secondary tunneling which, again, is uniaxial. Again we say about which of the other three N-D bonds it takes place. The secondary tunneling frequency is only 4.5 kHz. The deuteron of NH3D+ ions gets localized at T<25 K. It can reside in any of the four sites available to the hydrogens of the ion. The dynamics of the three protons depends strongly on which site the deuteron occupies. If it is the site which was identified as unique for ND4+ ions, the protons reorient stochastically with a rate k>10(6) s(-1). Very likely, they also undergo tunneling but the stochastic reorientations erase any tunneling features from the spectra. By contrast, if the deuteron occupies any other site, stochastic reorientations of the protons are slow and (proton) tunneling on the scale of 10(5) Hz can be identified. Finally, isotopic ordering is observed. The single deuteron of NH3D+ ions goes preferentially into the site identified as unique. Energetically, the preference amounts to 1 meV.