A calculation of the electronic structure of (Hg,Cd)Te alloys in the coherent‐potential approximation (CPA) is presented. The problem is divided into three tasks: determining accurate band structures including relativistic terms for the constituent compounds (HgTe and CdTe), characterizing the alloy disorder, and executing the alloy calculation. These tasks are facilitated through the use of a set of symmetrized, orthonormal, local orbitals. We shall introduce the calculational procedure and discuss the results obtained to date. These include the calculated band structures for HgTe and CdTe, the local alloy disorder parameters, the alloy band energies, and density of states calculated in the virtual crystal approximation and in a simplified version of CPA.