  The energy spectrum of the valence band in HgTe/Cd$_x$Hg$_{1-x}$Te quantum
wells with a width $(8-20)$~nm has been studied experimentally by
magnetotransport effects and theoretically in framework $4$-bands $kP$-method.
Comparison of the Hall density with the density found from period of the
Shubnikov-de Haas (SdH) oscillations clearly shows that the degeneracy of
states 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 the
calculations of the spectrum performed within the framework of the $4$-bands
$kP$-method for symmetric quantum wells. These calculations show that the top
of the valence band consists of four spin-degenerate extremes located at $k\neq
0$ (valleys) which gives the total degeneracy $K=8$. It is shown that taking
into account the "mixing of states" at the interfaces leads to the removal of
the spin degeneracy that reduces the degeneracy to $K=4$. Accounting for any
additional asymmetry, for example, due to the difference in the mixing
parameters at the interfaces, the different broadening of the boundaries of the
well, etc, leads to reduction of the valleys degeneracy, making $K=2$. It is
noteworthy that for our case two-fold degeneracy occurs due to degeneracy of
two single-spin valleys. The hole effective mass ($m_h$) determined from
analysis of the temperature dependence of the amplitude of the SdH oscillations
show that $m_h$ is equal to $(0.25\pm0.02)\,m_0$ and weakly increases with the
hole density. Such a value of $m_h$ and its dependence on the hole density are
in a good agreement with the calculated effective mass.
