Abstract Metal–insulator–semiconductor structures based on HgCdTe are grown by molecular-beam epitaxy. Near-surface graded-gap layers with a high CdTe content are inserted on both sides of the epitaxial HgCdTe film. The capacitance–voltage characteristics of these structures are studied experimentally. The main characteristics of these graded-gap HgCdTe structures are determined taking into account the effect of the non-uniform composition of the near-surface layers on the measured parameters. The capacitance–voltage characteristics of the graded-gap HgCdTe structures with various insulators are examined and the densities of surface states, densities of fixed and mobile charges are evaluated. The properties of the interface for CdTe grown in situ are found to be fairly good. We found that for structures based on HgCdTe–CdTe typical of very low density of mobile charges, the density of fixed charge does not exceed a 5.5 × 10 10 cm − 2 .