We report on the molecular-beam epitaxy of ZnBeSe ternary alloys lattice matched onto GaAs substrates. We demonstrate that these alloys can be grown with a high structural perfection. X-ray linewidths down to 27 arcsec are obtained even though the growth is carried out on bare substrates. Transmission electron microscopy reveals the high quality of the interface. Photoluminescence spectra of undoped layers are dominated by free-exciton recombinations. The excitonic gap is determined to be 2.863 eV at 9 K. Finally, high carrier concentrations are obtained for bothn-type andp-type doping. These results are promising in view of fabricating laser diodes with this material system. ©1997 American Institute of Physics.