Abstract: A method for growing II-VI semiconductor crystals and II-VI semiconductor layers as well as crystals and layers of their ternary or quaternary compounds from the liquid or gas phase is proposed. To this end, the solid starting materials are introduced into a growing chamber for the growing of crystals. Inside the growing chamber, carbon monoxide is supplied by way of reducing agent. At least certain zones of the growing chamber are heated to a temperature at which a first-order phase transition of the starting materials takes place and the starting materials pass into the liquid or gas phase. The starting materials are then cooled down accompanied by the formation of a semiconductor crystal or semiconductor layer, again with a first-order phase transition taking place. The oxygen present in the growing chamber is bound by the carbon monoxide and the formation of an oxide layer at the phase boundary of the growing semiconductor crystal or semiconductor layer is prevented.