  We study the effects of electron-hole asymmetry on the electronic structure
of helical edge states in HgTe/HgCdTe quantum wells. In the framework of the
four-band kp-model, which takes into account the absence of a spatial inversion
centre, we obtain analytical expressions for the energy spectrum and wave
functions of edge states, as well as the effective g-factor tensor and matrix
elements of electro-dipole optical transitions between the spin branches of the
edge electrons. We show that when two conditions are simultaneously satisfied
-- electron-hole asymmetry and the absence of an inversion centre -- the
spectrum of edge electrons deviates from the linear one, in that case we obtain
corrections to the linear spectrum.
