The present investigation is devoted to the further study of the two-temperature evaporation-condensation-diffusion (ECD) method. Experiments have been performed to determine the Hg vapour pressure influence on rates of HgTe evaporation and condensation, morphological peculiarities of the initial stages of Hgzeta-xCdxTe layer growth, and interdiffusion in the HgTe-CdTe system. It is shown that the classical ECD method for Hg vapour pressures higher than 4 atm becomes inefficient due to the several reasons discussed in this paper. We suggest a two-stage epitaxy process for Hg1-xCdxTe and other solid solutions. In the first stage, a structurally perfect layer with a desired thickness is formed at low Hg pressure. In the second stage, the Hg vapour pressure is fixed. This provides the necessary composition of the layer surface. High-quality Hg1-xCdxTe layers with the surface composition x(s) up to 0.5 are reproducibly obtained by this proposed technique.