A comparative study is made of the influence of high pressures (15-50 GPa) on the conductance of the ammonium halides NH4X (X=F, Cl, Br) at temperatures of 77 K and above. It is found that the application of high pressure induces a phase transition which is manifested in a sharp (jumplike) change in the resistance by several (more than three) orders of magnitude and is accompanied by hysteresis typical of a first-order phase transition. The values of the pressure Pc1 correlate with the density of the material and are approximately 40, 27, and 15 GPa for NH4F, NH 4Cl, and NH4Br, respectively. The relaxation times of the resistance depend strongly on the pressure: in the transition region the relaxation time is increased significantly (from several hours to days). At pressures much higher than Pc1 it is several minutes.