The binary systems Ca-5[PO4](3)F-CaAl2Si2O8 and Ca-5[PO4](3)F-CaMgSi2O6 have been investigated, via annealing and quenching in the experimental method, direct observation of the melting behavior of the samples, X-ray diffraction analysis, petrography, and transmission electron microscopy. Phase equilibrium in the ternary system Ca-5[PO4](3)F-CaAl2Si2O8-CaMgSi2O6 was determined by combining information from the structure of the binary boundary systems and additional experimental data that were obtained from ternary compositions. The glass-formation region of the fluorapatite-anorthite-diopside system was studied, and the glass compositions for the development of glass-ceramics for technical and medical applications were identified.