We have performed an Extended X-ray Absorption Fine Structure (EXAFS) measurement of Cd1-x Mn x Te and Cd1-xZnx Te semiconductor alloys for various concentrations x. We have found well-defined different nearest-neighbor Cd-Te, Mn-Te and Zn-Te distances almost independent of x. We have developed a model of the microscopic structure of the zinc-blende-type A1-xBxC ternary alloys based on a random distribution of cations, which describes perfectly the bimodal distribution of near-neighbor distances in terms of distortion of the anion sublattice using the lattice constant of the alloy and the bond-stretching constants of each binary component. Within the framework of this model we discuss also the problem of the structural stability of Cd1-xMnx...