The conditions for growing bulk alpha-BaB2O4 single crystals from stoichiometric melts and high-temperature solutions as well as some associated problems are reported. The morphology of crystals, formation Of inclusions and light,scattering depending on crystal growth condition,.; are described. Comparative estimation of spectral characteristics and of the optical quality. as well as the damage threshold of crystal samples suitable for production of polarization devices of laser systems have been performed. (C) 2002 Elsevier Science B.V. All rights reserved.