Abstract: Monocrystals based on zirconium or hafnium dioxide stabilized with yttrium oxide having the following proportions of the said elements (in mol. %)Zirconium or hafnium dioxide: 70-90Yttrium oxide: 30-10.Said monocrystals may also contain oxides of the transition or the rare-earth elements or their mixtures in an amount of from 0.01 to 5% of the weight of the monocrystal.The method of producing the monocrystals consists in the preparation of a charge of zirconium or hafnium dioxide and yttrium oxide, melting of the charge, and growing the monocrystals from the obtained melt in the open air by the Stockbarger process.The obtained monocrystals obtained are transparent, colorless, have a high optical quality (a refractive index of n =2-2.2; a transmission band of 2,000-74,000 A), a microhardness of 1,300 to 1,500 kg/mn.sup.2, a dislocation density of 10.sup.3 to 10.sup.5 cm.sup.-2, and with various dimensions (a height of 1 to 8 cm, and a cross section of 0.5 to 4 cm.sup.2).