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A first-principles method based on density functional theory (DFT), a generalized gradient approximation (GGA),and a projector-augmented wave (PAW) are used to study the structuai and band properties of wurtzite Zn1-xCdxO and Zn1-xMgxO (0 ≤x ≤1) teary alloys. By taking into account all of the possible structures, the band gaps of Zn1-xCdxO and Zn1-xMgxO alloys are corrected and compared with experimental data.