  We investigate the electron states in double asymmetric
$\rm{HgTe/Cd_{x}Hg_{1-x}Te}$ quantum wells grown along the $[001]$ direction.
The subbands are computed by means of the envelope function approximation
applied to the 8-band Kane $\bf{k}\cdot\bf{p}$ model. The asymmetry of the
confining potential of the double quantum wells results in a gap opening which
is absent in the symmetric system where it can only be induced by an applied
electric field. The band gap and the subbands are affected by spin-orbit
coupling which is a consequence of the asymmetry of the confining potential.
The electron-like and hole-like states are mainly confined in different quantum
wells, and the enhanced hybridization between them opens a spin-dependent
hybridization gap at a finite in-plane wavevector. We show that both the ratio
of the widths of the two quantum wells and the mole fraction of the
$\rm{Cd_{x}Hg_{1-x}Te}$ barrier control both the energy gap between the
hole-like states and the hybridization gap. The energy subbands are shown to
exhibit inverted ordering, and therefore a nontrivial topological phase could
emerge in the system.
