Reflectance and photoluminescence spectra of the ZnO/Zn0.78Mg0.22O structures with ZnO quantum wells and thick ZnO and Zn0.78Mg0.22O layers have been thoroughly investigated at different temperatures and excitation intensities and wavelengths. All the observed spectral lines have been identified. It has been established that the built-in electric field does not affect the spectrum as strongly as was expected. The built-in field is apparently effectively screened by the carriers that have migrated to the bands from donor and acceptor levels. The parameters determining the exciton properties in zinc oxide have been estimated.