In this research, density functional theory accompanied with linear combination of atomic orbitals (LCAO) method is applied to study the atomic and electronic structure of wurtzite and rocksalt ZnxMg1−xO pseudobinary compounds in their bulk phases. Calculated band gaps of ZnxMg1−xO solid solutions under study are further validated by means of spectroscopic ellipsometry and optical absorption. In agreement with an experiment, it is predicted that increase of Zn content in ZnxMg1−xO leads to narrowing of its band gap for both wurtzite and rocksalt phases. The calculated infra-red (IR) spectra show that the IR peaks are shifted towards larger frequencies along with decrease of Zn content. Presence of imaginary phonon frequencies in rocksalt ZnxMg1−xO of x > 0.625 allows us to suggest that it is necessary to use properly oriented substrates for epitaxial growth to overcome polycrystallinity inZnxMg1−xO thin films at concentration x = 0.4 – 0.6.