Bound states in inversion layers on p-Hg//1// minus //xCd//x Te are calculated self-consistently taking the interaction of the conduction and valence bands through the surface potential and the kappa multiplied by (times) rho interaction explicitly into account. Three different models of the band structure are compared and numerical results are presented. It is shown that the four-band spinless model, proposed by Zawadzki for InSb, is not appropriate to describe the bound states on Hg//1// minus //xCd//x Te and more elaborate models, which take the spin - orbit interaction into account, have to be used.