From previous studies it is known that alpha-tertiary calcium phosphate (α-TCP), monocalcium phosphate monohydrate (MCPM) and calcium oxide form cements upon mixing combinations of them with water. In this study some formulations were optimized with respect to the particle size of the constituents, their molar ratio, amounts of hydroxyapatite or beta-tertiary calcium phosphate (β-TCP) added and the water/powder ratio. Three suitable products were obtained. Product 1 had a relatively short setting time and might be suitable as a dental cavity liner or for filling parodontological pockets or for filling alveolar cavities to prevent alveolar ridge resorption. Products 2 and 3 may be more suitable for orthopaedic purposes. Their compressive strength being 35 and 12 MPa, respectively, after soaking for 1 day in Ringer's solution at 37°C. Product 1 reaches its full strength within 4 h, whereas products 2 and 3 take about 12 h and 10 h, respectively.