ZnO 1Àx Y x with chalcogen element Y exhibits intriguing optoelectronic properties as the alloying strongly impacts the band-gap energy E g (x). In this work, we analyze and compare the electronic structures and the dielectric responses of Zn(O,S) and Zn(O,Se) alloys by means of the density functional theory and the partially self-consistent GW approach. We model the crystalline stability from the total energies, and the results indicate that Zn(O,S) is more stable as alloy than Zn(O,Se). We demonstrate also that ion relaxation strongly affects total energies, and that the band-gap bowing depends primarily on local relaxation of the bonds. Moreover, we show that the composition dependent band-gap needs to be analyzed by the band anti-crossing model for small alloying concentration, while the alloying band-bowing model is accurate for strong alloying. We find that the Se-based alloys have a stronger change in the band-gap energy (for instance, DE g (0.50) ¼ E g (ZnO)-E g (x ¼ 0.50) % 2.2 eV) compared with that of the S-based alloy (DE g (0.50) ¼ 1.2 eV), mainly due to a stronger relaxation of the Zn-anion bonds that affects the electronic structure near the band edges. The optical properties of the alloys are discussed in terms of the complex dielectric function e(x) ¼ e 1 (x) þ ie 2 (x) and the absorption coefficient a(x). While the large band-gap bowing directly impacts the low-energy absorption spectra, the high-frequency dielectric constant e 1 is correlated to the intensity of the dielectric response at energies above 4 eV. Therefore, the dielectric constant is only weakly affected by the non-linear band-gap variation. Despite strong structural relaxation, the high absorption coefficients of the alloys demonstrate that the alloys have wellbehaved optoelectronic properties. V