The behaviour of ammonium ions in the mixed crystals of alkaline metal-ammonium halides until present time are not fully understood. There are the observations at low temperature of the low energy resonance modes in the disordered α-phase of the K1-x(NH4I mixed crystals which are observed also in orientational glass state of this phase. However, low energy resonance modes are not observed in the low temperature ordered phases of these mixed crystals. The identification of the origin of the resonance modes in the K0.55(NH4)0.45I mixed crystal was carried out with the help of the inelastic incoherent neutron scattering from protonated and deuterated samples. It was shown that these modes can be treated as translational. The study also was carried out of the influence of the transfer from the static orientationally disordered glass state into die dynamic orientationally disordered state in the α-phase of protonated K0.55(NH4)0.45I mixed crystal with the temperature increase on the evolution of the inelastic incoherent neutron scattering intensity.