The system (NH 4 ) x K 1−x I is known to possess a variety of low-temperature phase transitions, depending on the concentration x. We investigated the phase diagram of the deuterated homologues for x = 0.35, 0.5 and 0.7 by powder neutron diffraction in dependence on temperature and under applied pressures of up to 1.4 GPa. Under ambient conditions, (ND 4 ) x K 1−x I shows the same NaCl-type structure (α-phase) as its protonated homologues. A transition into a primitive cubic high-pressure phase corresponding to the so-called β-phase has been detected, which is characterized by a CsCl-type structure for all the concentrations investigated here. The transition is of first order and completely reversible. In contrast to the behaviour under applied pressure, the phase diagram in dependence on temperature is similar to that of the protonated homologues. In particular, the sample with x=0.35 shows a behaviour indicative of glass forming properties, whereas the x=0.7 sample exhibits two low-temperature phase transitions.