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A new type of oxyfluoride glass-ceramics based on the silicate glassy matrix and the nano-phase of LaF3 was developed for generating the up-conversion luminescence processes. In such material, the low-phonon energy crystals of LaF3 are desirable host for the rare-earth elements. The effect of admixture of 3 mol% of La2F6 on the structural changes of glasses in the Na2O–B2O3–SiO2 system was investigated. The effect of LaF3 additive was studied using 29Si, 11B, and 23Na MAS NMR to learn more about the structural role of modifiers as well as fluorine in the glassy matrix. Glasses with compositions corresponding to different B2O3/Na2O and B2O3/(Na2O + 3La2F6) ratios in the 0.6–1.2 range were obtained by melt quenching. The 29Si MAS NMR spectra indicated that the [SiO4] units are more polymerized when the ratios and the fluorine admixture increase. The 11B NMR spectra revealed the presence of both [BO4] (Q4) and [BO3] (Q3) units. The fraction of Q3 increased with the decreasing sodium content. Glasses with the LaF3 additive showed higher BO3/BO4 ratios. The effect of thermal treatment for glasses with the tendency towards LaF3 crystallization was discussed in terms of structural changes.