The local structural properties of Hg1−xCdxTe, Hg1−xZnxTe, and Cd1−xZnxTe are examined using a self-consistent pseudopotential approach. An accurate description of the limiting crystals is obtained by adding empirical corrections to ab initio total energies calculated with the group-II d states included in the cores. Similar calculations for x=0.5 ordered alloys confirm the presence of nearest-neighbor bond-length differences in these systems without violation of Vegard’s law. An anomalously large ‘‘relaxation’’ is predicted here for Hg1−xCdxTe (∼2% bond-length difference in the alloy compared to only 0.3% between limiting crystals) due to the dominance of chemical effects neglected from simple valence force models. The implications of the present results for alloy mixing energies and possible deviations from randomness are discussed.