Structural and electronic properties of MgZnO and BeMgZnO alloys are studied by the ab-initio Density Functional Theory method. Large band gap bowings are found for both kinds of alloys. The total energies as functions of the lattice constants are calculated and used to determine the ranges of composition in which the alloys are stable in the wurtzite structure. It is shown that the addition of 6% of Be can already help in stabilization of the MgZnO alloy in the wurtzite structure. The band gap can reach 7 eV for the wurtzite BexMg0.5Zn0.5-xO alloys with x approaching 0.5 and about 5.0 eV for Be0.125MgxZn0.875-xO type alloys for x approaching 0.6. Varying the alloy composition according to the presented stabilization diagram showing ranges of the x, y, for which BexMgyZn1-x-yO is stable in the wurtzite phase, one may tune band gaps over a wide spectral range, which provides flexibility in band gap engineering.