Polarizaton properties of ZnO well layers on BeMgZnO barrier layers grown in polar and semipolar orientations have been investigated. Cases of relaxed and strained barrier layers are considered. It is found that the polarizaton difference at the interfaces leads to a built-in electric field inside the well layer as much as 8 MV cm^(-1) in magnitude. Nonpolar ZnO/BeMgZnO quantum wells have been studied in terms of intersubband transitions. The calculations have covered Be and Mg concentrations up 0.18 and 0.5, respectively. It has been found that intersubband transition (ISBT) energies ranging from 50 to 700 meV are possible. The effect of barrier thickness on the ISBT energies has been studied. The results indicate insignificant changes in ISBT energies compared to the energies.