The phase stabilities and structural and electronic properties of three zinc-based oxide alloy systems (Ca(x)Zn(1-x)O, Cd(x)Zn(1-x)O and Mg(x)Zn(1-x)O) are studied by first-principle methods. We examine all alloy configurations in three 16-atom supercells (1 × 1 × 2 B1 phase structure, 2 × 2 × 1 and 2 × 1 × 2 B4 phase structures) and utilize symmetry of the bulk materials to reduce the amount of calculation. Taking into account the contribution of the alloy statistics, we have drawn the regions of phase stability for Ca(x)Zn(1-x)O (0.25<x<0.375), Mg(x)Zn(1-x)O (0.375<x<0.5) and Cd(x)Zn(1-x)O (0.75<x<0.875). We have also analyzed lattice constants (a and c), structural parameter u and the bond lengths in the wurtzite phases. We found that the averaged lattice constants of Mg(x)Zn(1-x)O and Ca(x)Zn(1-x)O do not follow the Vegard rule and this is related to the degree of instability of the wurtzite MgO and CaO. Wurtzite CaO is not stable and turns into hexagonal CaO upon geometry optimization. The calculated band gaps are found to be consistent with the experimental values for alloys Cd(x)Zn(1-x)O and Mg(x)Zn(1-x)O. The bowing parameters for alloys Mg(x)Zn(1-x)O and Cd(x)Zn(1-x)O are estimated to be 0.87 and 1.30 eV, respectively.