The materials with the common chemical formula AII BV3 2 differ itself by diverse crystalline forms. Their anion sublattices are similar to FCC, but just three quarters of the tetrahedral voids are filled by metal atoms. So, the matter here is the stoichiometric vacancies. The diverse manners of the vacancies ordering define the features of all of the crystalline forms. The chain of the transformations β →α ′′→α ′→α is the subject of our report. Even though this chain has been already considered within the model with three structural fragments in [1], the results of [1] ought to be yet confirmed in framework of the model [2] with four fragments. These four structural fragments are anti- 2 3 Ag O type, whereas authors [1] deal with the fragments of anti-fluorite type and two types of sphalerite fragments. A model of a fragment of the structure of the β -modification is presented on the fig.1. The cations occupy “randomly” only six of eight tetrahedral emptinesses among the anions on the one hand. On the other hand, both vacant emptinesses are located strictly along one of four spatial diagonal of the cubic fragment. The model described here is known as the lattice of anti – 2 3 Ag O type [2]). The prefix (“anti”) has meaning solely of the interchange by seats between the cations and anion. It is assumed usually, that the four fragments alternate itself in cube disorderedβ - phase in casual order. The cell of first tetragonal phase (α ′′ ) contain two different layered packets ( X ,Y ). Each of them consist just of the two type of the fragments from the set of four possible. Moreover, the concerted transitions, like that illustrated by figure 1, should be separated into two classes. First of them are the transitions along the direction of the main crystalline axis. Such transitions does not change the kind of the layered packets, though they change the type of fragments. Opposite, the transitions in the plane of packets change their kind: X ↔Y . This observation indicates, that α ′′ -phase may be partly disordered in the plane of each packet as for the alternating of both fragments, whereas the packets alternate itself right along the main axis. These results are in accordance with the [1], where it has been pointed first time out that the transformation β →α ′′ provides the ordering of vacancies only partially. Thereto, such one-dimensional ordering of the two subjects ( X,Y ) allows the applying for β →α ′′ of the theory results for binary alloys, how it has been done in [1]. Then there are all grounds to suppose that the rest of the chain (i.e. the α ′′→α ′→α ) consist of the two typical polytipic transformations. First of them is accompanied by doubling of quantity of packages in a cell. Second of them is accompanied by the inversion of the structure of one of the four packets [1]. Now it is possible to do the conclusion about the accordance with results of [1] as for the nature of the ordering of vacancies in these materials. Undeniably there should be two kinds of ordering and first of them occurs at β →α ′′ transformations as for 3 2 3 2 3 2 3 2 Zn P ,Cd P , Zn As ,Cd As . Second of them realizes itself as two trivial polytypic transformations as for 3 2 3 2 Zn As ,Cd As . Hence, the results of [1] are confirmed in the framework of alternative structural model.figuraFig. 1. A cubic fragment of anti- 2 3 Ag O type: the projection on the (110)-plane. Two white arrows show the possible transitions inside united voids from one cations location to another possible.