High-quality Zn_1-xMg_xO alloys are found to be very efficient UV light emitters, even more efficient than ZnO, particularly in the high-temperature region. The emission band width and strength of the photoluminescence from Zn_1-xMg_xO alloys increase remarkably with increasing Mg concentration. We have revealed that the increase in the strength is mainly due to the increase in the activation energy required for the nonradiative recombination process. Therefore, it is suggested that the localization of excitons due to spacial fluctuation of the Mg concentration in Zn_1-xMg_xO alloys takes place, and that the degree of the localization increases as Mg concentration increases.