The impact of the presence of the near-surface graded-gap layers with an increased content of CdTe on the admittance of MIS structures based on MBE-grown n -Hg 1– x CdxTe ( x = 0.22–0.23) with the Al 2 O 3 insulating coating has been experimentally studied. It has been shown that the structures with a gradedgap layer are characterized by a deeper and wider capacitance dip in the low-frequency capacitance–voltage (CV) characteristic and by higher values of the differential resistance of the space-charge region than the structures without such a layer. It has been found that the main features of the hysteresis of capacitance dependences typical of the graded-gap structures with SiO 2 /Si 3 N 4 are also characteristic of the MIS structures with the Al 2 O 3 insulator. The factors that cause an increase in the CV characteristic hysteresis upon formation of the graded-gap layer in structures with SiO 2 /Si 3 N 4 or Al 2 O 3 are still debatable, although it may be assumed that oxygen plays a certain role in formation of this hysteresis.