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Bone mineral has a composition very similar to Ca10(PO4)6(OH)2 (hydroxyapatite-HA), but, additionally, contains several ionic substitutions. Since the resorption rate of HA is too low to induce massive bone growth, biphasic calcium phosphate ceramics, combinations of -Ca3(PO4)2 (tricalcium phosphate) and HA, are commonly used as bioactive implants. Another way to improve resorptivity of such materials is chemical modification of HA or Ca3(PO4)2, e.g. by Ca/M (=alkaline metal) substitution leading to formation of CaMPO4 compounds with rhenanite structure. The main objective of this study was to create materials with better resorption properties compared to HA. We have chosen double phosphates of calcium and alkaline metals Ca(3-x)М2x(PO4)2 (x=0÷1, М=Na, K) with crystal structure of β-Ca3(PO4)2 (х<0.15) and β-CaNaPO4 (x=1) as the components of ceramics and multiphase composites. The phase diagrams of the systems Ca3(PO4)2-CaNaPO4 and Ca3(PO4)2-CaKPO4 have been studied. Phase diagram of Ca3(PO4)2-CaNaPO4 was verified according to the literature. Phase «A» - a solid solution near the composition Ca5Na2(PO4)4, was considered as a superlattice of CaNaPO4 with doubled a lattice parameter and tripled c. Also, kinetics of α↔β transformation in pure Ca3(PO4)2 and CaNaPO4 were explored, and critical cooling rate to produce single-phase Ca3(PO4)2 was determined. Phase diagram of Ca3(PO4)2-CaKPO4 system has been constructed for the first time. The main feature of it compared to the sodium system is an area of solid solution, called us by «B», at the vicinity of the composition with x=0.33 considered as a superstructure of CaKPO4. The solid solution «B» is transformed to apatite-like phase called us by «X» under cooling. Solubility of the ceramic materials was investigated. The solubility of materials with high amount of high-temperature rhenanite phases is increased in comparison with materials based on β-Ca3(PO4)2.