The two-dimensional electron gas in the surface layers of HgMnTe with inverted bands is studied for the first time experimentally and theoretically. It is shown that the structure of the investigated capacitance magnetooscillations in HgMnTe MOS structures is entirely similar to that observed in the non-magnetic gapless semiconductor HgCdTe and the sole effect of the exchange interaction is the temperature shift of beat nodes. The information about the exchange pararmeters is obtained only from modeling the oscillations, because no pronounced changes in the position of oscillations are observed and the separate spin components are not resolved. For the description of the spectrum in the magnetic field, we propose a theory that takes the exchange and spin-orbit interactions into account for materials with direct and inverted bands. A comparison between experiment and theory for different temperatures and exchange intel action parameters is reported. The modeling shows that the spin-orbit splitting by far exceeds the contribution of the exchange interaction. The calculated amplitudes of "partial" oscillations for different spill branches of the spectrum are essentially different in accordance with the difference in the intensities of the corresponding lines in the Fourier spectra of the experimental oscillations. (C) 2001 MAIK "Nauka/Interperiodica".