Short description of important scientific result: A series of experimental works on the synthesis and study of the spectral properties of crystals of the type LiSrxCa1-xAlF6: Ce, LiCaAlF6, LiCaxSr1-xAlF6, crystals with double activation Ce + Yb, Ce + Cr, as well as crystals with the addition of a charge compensator Na + have been carried out. Structural and spectroscopic properties of crystals were studied by EPR, Raman, Z-scan methods. Crystals are of practical importance for the construction of laser systems, as evidenced by the obtained lasing on crystals: LiSr (50) Ca (50) AlF6: Ce 0.5%, LiSr (35) Ca (65) AlF6: Ce 0.5%, LiCaAlF6: Ce (1%) + Na (1%), LiCaAlF6: Ce (1%) + Yb (1%), LiCaAlF6: Ce (1%) + Cr (1%). A number of such new laser media have been obtained and their characteristics have been measured, and their performance has been demonstrated as active media of solid-state lasers in the UV region of the spectrum. The results were published in 13 papers, of which 5 are publications indexed in Scopus.