Beryllium chalcogenides are a new class of II-VI materials and promising candidates for UV/VIS applications. In this paper we analyse the optical properties of the quaternary BeMgZnSe system lattice matched to GaAs. We investigate the compositional dependence of the fundamental and higher energy gaps (E-0, E-1, E-2). The investigations are performed (a) experimentally by photoreflectance and by ellipsometry up to 9.5 eV and (b) theoretically by first principles band structure calculations within the virtual crystal approximation (VCA). The fundamental energy gap is found to vary from 2.7eV for ZnSe to 3.7eV for a (Be,Mg)-content of 70%. The VCA calculations predict the correct overall gap dependencies. Especially, a negative bowing of the E-0 gap is predicted by the VCA model. This unusual behaviour may be explained by the absence of bond length redistribution dynamics in this lattice matched system.