The energy transfer between different pairs of lanthanide ions bonded by fluoride bridges into labile binuclear complexes is studied in aqueous solution at different ratios between the concentrations of lanthanide ions and fluoride anions ([Ln]: [F]). It is shown that, if the concentrations [Ln] and [F] are of the same order of magnitude, the energy transfer rate constant kt does not depend on the choice of the pairs of interacting ions and is determined by the association rate constant of Ln(III) ions into binuclear complexes. If the concentration of the lanthanide ions is much greater than that of the fluoride ions, kt varies proportionally to the monomolecular energy transfer rate constants in the binuclear complexes. It is assumed that, in the first case, Ln(III) ions are bonded through two fluoride anions, whereas, in the second case, they are bonded through one anion. The analysis of the variations in kt in the latter systems shows that the exchange-resonance mechanism should be taken into account for the explanation of the experimental data. The effects that the introduction into the solution of different contents of salts of strong acids—AlCl3, MgCl2, Ca(NO3)2, CsCl, RbBr, and NaCl—have on kt and on the regularities of the energy transfer between Ln(III) ions bonded into binuclear fluoride complexes are studied. The effects of these electrolytes on the luminescence intensity and spectrum of Eu(III) ions and on the values of kt for the energy transfer between Ln(III) ions bonded into binuclear complexes are analyzed. It is shown that, at some concentration ratio [Ln]: [F], for all electrolytes studied except AlCl3, the value of kt increases despite the fact that the concentration of mononuclear complexes of Ln(III) ions with fluorine decreases in the presence of these electrolytes. It is ascertained that the anions of strong acids in the outer sphere of lanthanide ions increase the association constant of Ln(III) ions in binuclear fluoride complexes.