Owing to wide range bandgap tunability to more than 5 eV, the quaternary (Be,Mg)ZnO solid solutions are attractive for a variety of UV optoelectronic applications, inclusive of solar blind photodetectors, and intersubband transition devices. The mutual compensation effects of Be and Mg on the formation energy and strain allows a wide range of compositions and bandgaps beyond those achievable by MgZnO and BeZnO ternaries. Localization effects are well pronounced in such wide-bandgap semiconductor alloys due to large differences in metal covalent radii and the lattice constants of the binaries, resulting in strain-driven compositional variations within the film and consequently large potential fluctuations, in addition to that possibly caused by defects. However, carrier localization may suppress recombination through nonradiative channels, and thus, facilitate high-efficiency optoelectronic devices. To investigate potential fluctuations and localization in BexMgyZn(1-x-y)O films grown by plasma-assisted molecular beam epitaxy, optical absorption and steady-state and time-resolved photoluminescence (PL) measurements were performed. O-polar BexMgyZn(1-x-y)O samples grown on GaN templates with compositions up to x = 0.04 and y = 0.18 were used for timeresolved studies, and O-polar BexMgyZn(1-x-y)O samples grown on sapphire with compositions up to x = 0.19 and y = 0.52 were used for absorption measurements. From spectrally resolved PL transients, BeMgZnO samples with higher Mg/Be content ratio were found to exhibit smaller localization depth, Δ0=98 meV for Be0.04Mg0.17Zn0.79O and Δ0=173 meV for Be0.10Mg0.25Zn0.65O, compared to samples with smaller Mg/Be ratio, Δ0=268 meV for Be0.11Mg0.15Zn0.74O. Similar correlation is observed in temporal redshift of the PL peak position of 8 meV, 42 meV and 55 meV for Be0.04Mg0.17Zn0.79O, Be0.10Mg0.25Zn0.65O and Be0.11Mg0.15Zn0.74O, respectively, that originates from potential fluctuations and removal of band filling effect in the localized states. PL transients indicate that emission at low temperature is dominated by recombination of localized excitons, which exhibit decay times as long as τ = 0.36 ns at the peak position. The Sshaped behavior of PL peak with change in temperature was observed for the quaternary alloy Be0.04Mg0.17Zn0.79O. The degree of localization σ was determined to be 22 meV. Relatively high potential fluctuations and localization energy lead to a strong Stokes shift, which increased with bandgap reaching ~0.5 eV for O-polar BeMgZnO on sapphire with 4.6 eV absorption edge.