Pseudobinary heterostructural alloys of ZnO with MgO or CdO are studied by composing the system locally of clusters with varying ratio of cations. We investigate fourfold (wurtzite structure) and sixfold (rocksalt structure) coordination of the atoms. By means of density functional theory we study a total number of 256 16-atom clusters divided into 22 classes for the wurtzite structure and 16 classes for the rocksalt structure for each of the alloy systems. The fraction with which each cluster contributes to the alloy is determined for a given temperature T and composition x within (i) the generalized quasi-chemical approximation, (ii) the model of a strict-regular solution, and (iii) the model of microscopic decomposition. From the cluster fractions we derive conclusions about the miscibility and the critical compositions at which the average crystal structure changes. Thermodynamic properties such as the mixing free energy and the mixing entropy are investigated for the three different statistics. We discuss the consequences of the two different local lattice structures for characteristic atomic distances, cohesive energies, and the alloys' elasticities. The differences in the properties of Mg x Zn 1−x O and Cd x Zn 1−x O are explained and discussed.