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The energy spectrum of the valence band in HgTe/Cd$_x$Hg$_{1-x}$Te quantumwells with a width $(8-20)$~nm has been studied experimentally bymagnetotransport effects and theoretically in framework $4$-bands $kP$-method.Comparison of the Hall density with the density found from period of theShubnikov-de Haas (SdH) oscillations clearly shows that the degeneracy ofstates of the top of the valence band is equal to 2 at the hole density $p<5.5\times 10^{11}$~cm$^{-2}$. Such degeneracy does not agree with thecalculations of the spectrum performed within the framework of the $4$-bands$kP$-method for symmetric quantum wells. These calculations show that the topof the valence band consists of four spin-degenerate extremes located at $k\neq0$ (valleys) which gives the total degeneracy $K=8$. It is shown that takinginto account the "mixing of states" at the interfaces leads to the removal ofthe spin degeneracy that reduces the degeneracy to $K=4$. Accounting for anyadditional asymmetry, for example, due to the difference in the mixingparameters at the interfaces, the different broadening of the boundaries of thewell, etc, leads to reduction of the valleys degeneracy, making $K=2$. It isnoteworthy that for our case two-fold degeneracy occurs due to degeneracy oftwo single-spin valleys. The hole effective mass ($m_h$) determined fromanalysis of the temperature dependence of the amplitude of the SdH oscillationsshow that $m_h$ is equal to $(0.25\pm0.02)\,m_0$ and weakly increases with thehole density. Such a value of $m_h$ and its dependence on the hole density arein a good agreement with the calculated effective mass.

The valence band energy spectrum of HgTe quantum wells with inverted band structures