Owing to its large bandgap covering the UV region of the optical spectrum, the quaternary BeMgZnO is of interest, particularly the collective effect Be and Mg fluxes on the solid composition. Incorporation of Be, Mg, and Zn in the wurtzite BeMgZnO quaternary alloy was found to depend strongly on the reactive-oxygen to metal flux ratio during growth by plasma-assisted molecular beam epitaxy under metal-rich conditions. For a given set of metal fluxes, reducing the VI/II (oxygen to metal flux) ratio from 1.0 to 0.6 increased the bandgap from 4.0 eV to 4.5 eV and decreased the c lattice parameter from 5.08 angstrom to 5.02 angstrom. The corresponding change in composition from Be0.07Mg0.21Zn0.72O to Be0.10Mg0.34Zn0.56O was consistent with a systematic reduction in the Zn incorporation coefficient from 0.23 to 0.12, while those of Be and Mg remained at similar to 1. This behavior was explained by the substantially lower formation enthalpies of wurtzite BeO and MgO, -5.98 eV and -5.64 eV, respectively, compared to that of ZnO, -3.26 eV, determined using first principles calculations, as well as the high equilibrium vapor pressure of Zn, which results in re-evaporation of excessive Zn from the growing surface, details of which are the topic of this manuscript. (C) 2017 Elsevier B.V. All rights reserved.