We have studied the heteroepitaxial growth of Be(Zn)Se alloys on both GaAs and Si substrates. The growth onto silicon shows many difficulties which are not completely solved yet. In contrast, on GaAs substrates, good crystalline quality is obtained even for layers with lattice misfit as high as 4%. p-Type doping with N-A-N-D of 2 x 10(17) cm(-3) has been achieved fur Be0.17Zn0.83Se (E-a = 3.18 eV). The optical properties of these alloys have been investigated using reflectivity, photoluminescence and vacuum UV ellipsometry. Ellipsometric studies of BeSe grown onto Si supports the indirect nature of the gap and confirms the position of the fundamental gap around 5.5 eV. The variation of the optical properties in BeZnSe alloys reveals the existence of a singularity around 46% which is attributed to a change in the band-gap nature nature.