We analyze the influence of the Mg concentration on several important properties of the band structure of Zn1-xMgxO alloys in wurtzite structure using ab initio calculations. For this purpose, the band structure for finite concentrations is defined in terms of the Bloch spectral density, which can be calculated within the coherent potential approximation. We investigate the concentration dependence of the band gap and the crystal-field splitting of the valence bands. The effective electron and hole masses are determined by extending the effective mass model to finite concentrations. We compare our results with experimental results and other calculations.