Low resistance ohmic contacts to p-ZnSe involving the use of HgSe are studied in detail. HgSe does not form an ohmic contact with p-ZnSe because of a residual valence band offset at the heterojunction of 0.5 to 0.6 eV. Annealing of HgSe/ZnSe : N does not result in an ohmic contact because a large miscibility gap in Hg,-,Zn,Se prevents a Hg-Zn interdiffusion and therefore the formation of a graded heterojunction. The molecular beam epitaxial (MBE) growth of Hg, -,Zn,Se does not circumvent this problem because these epitaxial layers suffer from a compositional phase separation due to spinodal demixing during MBE growth. A significant improvement of HgSe based contacts could be achieved by the use of ZnSe, -,Te,:N transition layers between HgSe and ZnSe : N. Either by abrupt, graded, or multilayer heterojunctions, very low contact resistivities are obtained. The growth of ZnSe, -,Te,: N layers on top of ZnSe: N is shown to reduce the carrier concentration in ZnSe : N by several orders of magnitude. A nitrogen diffusion process is believed to be responsible for this effect.