The stability constants (β1(F)) of the monofluoro complex of Ce(III) and those (β1(Cl)) of the monochloride solvent-shared ion-pair of Ce(III) have been determined in mixed solvents of methanol and water at 0.10 and 1.00 mol dm−3 ionic strengths, respectively. The variation in the Ce3+–Cl− distance, which was calculated using the Born-type equation and the Gibbs’ free energy derived from β1(Cl), indicated a change in the coordination number (CN) of Ce3+ from CN = 9 to a mixture of CN = 9 and 8 in the vicinity of the mole fraction of methanol (Xs) = 0.23. The variation in ln β1(F) with an increase in Xs in the mixed-solvent system showed an acute-angled convex inflection point at Xs = about 0.22 and an acute-angled concave inflection point in the vicinity of Xs = 0.28. It was concluded that the convex inflection point denoted the same change in the CN of Ce3+ from CN = 9 to a mixture of CN = 9 and 8, and that the concave point was a change in the CN of Ce(III) in CeF2+ from CN = 9 to a mixture of CN = 9 and 8.