 This is a single BNCT-facility, non-randomized, non-comparative, prospective, open-label, phase III study to determine the value of BNCT in the treatment of inoperable, irradiated, progressing anaplastic astrocytomas or glioblastomas following conventional radiation therapy. The neutron irradiation site is the FiR 1 reactor site, located at Otaniemi, Espoo, Finland, about 6 kilometers from the Helsinki University Central Hospital, Helsinki, where patient evaluation and post-irradiation care will take place. 