Epitaxial (Zn1−xMgx)1−yMnyO thin films were grown on c-Al2O3 substrates by radio frequency oxygen plasma assisted molecular beam epitaxy. Single crystal structure of the (Zn1−xMgx)1−yMnyO films was revealed by reflection high energy electron diffraction and X-ray diffraction. The band gap of the films can be tuned dramatically with increasing the Mg concentration, while the onset energy of Mn-related mid-gap absorption band only shows a small blue shift. Photoconductivity measurements indicate the Mn-related mid-gap states in (Zn1−xMgx)1−yMnyO films can create free carriers and contribute to charge transfer transitions. The conduction band offset ΔEC = 0.13 eV and valence band offset ΔEV = 0.1 eV were obtained for ZnO/Zn0.8Mg0.2O heterostructures, which increase to ΔEC = 0.21 eV and ΔEV = 0.14 eV for ZnO/Zn0.7Mg0.3O heterostructures.