The analysis of data obtained from the interband magnetoabsorption in HgSe and in mixed crystals Hg1-xCdxSe and HgSxSe1-x with compositions close to pure HgSe led the authors to the conclusion that in these materials mod E0 mod approximately=2/3 Delta where the energy gap E0=EGamma 6v-EGamma 8c and the spin-orbit splitting Delta =EGamma 8v-EGamma 7v. The results of the interband magnetoabsorption in the above mentioned materials could not be described in terms on the three-band Pidgeon-Brown model (1966), which provides a good description of the experimental data when mod E0 mod <2/3 Delta . In good order to interpret the magnetoabsorption data it was necessary to introduce a five-band model where the closest Gamma 15 'higher' band was explicitly taken into account. This model is used for the first time in the case of zero-gap semiconductors in a quantising magnetic field. Such a five-band model works well in Hg1-xCdxSe (x<0.01), oriented samples of HgSe (H//(001) and H//(111)) and HgSxSe1-x, x<0.05, always when mod E0 mod approximately=2/3 Delta (at helium temperature). Thus, a complete set of band parameters for Hg1-xCdxSe in the semimetallic region and HgSe are obtained. In particular, a peculiar character of the Gamma 6v level is described. Also for HgSxSe1-x the dependencies of fundamental band parameters on T and x were obtained by means of numerical fitting of the five-band model.