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Infrared spectroscopic ellipsometry in the spectral range from ω =360 cm-1 to ω =1500 cm-1 and Raman scattering spectroscopy are applied to study the long-wavelength optical phonon modes and dielectric constants of MgxZn1-xO thin films in the composition range 0≤x≤1. The samples were grown by pulsed laser deposition on sapphire substrates. X-ray diffraction measurements of the thin film samples reveal the hexagonal wurtzite crystal structure for x≤0.53 and the cubic rocksalt crystal structure for x≥0.67. A systematic variation of the phonon mode frequencies with Mg-mole fraction x is found for both hexagonal and cubic MgxZn1-xO thin films. The modified random isodisplacement model matches the observed composition dependence of the phonon mode frequencies for the hexagonal structure thin films [J. Chen and W. Z. Shen, Appl. Phys. Lett. 83, 2154 (2003)], whereas a simple linear approximation scheme is sufficient for the cubic structure part. We observe a discontinuous behavior of the transverse optical phonon modes (decrease), and the static and high-frequency dielectric constants (increase) within the phase transition composition region from the wurtzite structure part to the rocksalt structure part. On the contrary, the longitudinal phonon mode parameters increase almost linearly, and upon phase transition the splitting between the transverse and longitudinal modes increases. We associate this discontinuous behavior with the change of the nearest-neighbor coordination number from fourfold (wurtzite structure) to sixfold (rocksalt structure) in our samples and the associated increase in bond ionicity from ZnO to MgO. Accordingly, we propose that the reduced exciton mass parameter should approximately double upon changing from wurtzite to rocksalt crystal structure.