Until now, scientific work on the reactions of the complexation in water of fluoride ions with calcium or magnesium ions considered only soluble order 1 complexes (CaF+ and MgF+). The precipitation of the compounds CaF2 and MgF2 did not take into account the preliminary formation in solution of these order 2 complexes (CaF20 and MgF20). We therefore studied their formation using a direct potentiometric method in the F- ion-selective electrode at 25 degreesC. This experiment, together with a computerized thermodynamic study, allowed us to determine the values of formation constants at ionic strength equal to zero: log beta (CaF20) = 5.7 and log beta (CaF20) = 3.2, as well as limiting solubilities: S-CaF2 = 10(-4.8) and S-MgF20 = 10(-5) mol l(-1). Then, some examples were studied showing the necessity to take into account the formation constant of CaF2: the supersaturation of solutions, the validity of results from the fluoride selective electrode, the difference between released fluoride in distilled water and in artificial saliva in restorative dentistry, the fluoride concentration in hard waters and its health consequences. (C) 2000 Elsevier Science B.V. All rights reserved.