[en] An earlier statistical mechanical theory of complexing in molten mixtures of polyvalent metal halides and alkali halides is extended to situations in which an ionic equilibrium is established between two different types of complexes. The specific systems of interest are the mixtures of aluminium fluoride and sodium fluoride, in which early Raman scattering experiments by Gilbert, Mamantov and Begun have demonstrated coexistence of octahedral (AlF₆)^3- units and tetrahedral (AlF₄)^- units in the concentration range between 0.25 and 0.5 of AlF_3. Our treatment is based on a simple ionic model and involves (i) an evaluation of binding free energies for the two units in vacuo, showing that (AlF₆)^3- is strongly unstable against dissociation in this state, and (ii) a statistical mechanical theory of the liquid mixture, in which (AlF₆)^3- is stabilized by ionic screening interactions. The resulting ionic equilibrium in the liquid involves, in excellent agreement with the Raman data, strong suppression of dissociation for (AlF₆)^3-, except near the composition corresponding to criolite (AlF₃.3NaF). The temperature dependence of the ionic equilibrium is also evaluated, with special attention to molten criolite. Analogous calculations on aluminium-sodium chloride mixtures show that in these systems the equilibrium is completely shifted in favour of the (AlCl₄)^- species, as a consequence of its stabilization by halogen polarizability. (author). 13 refs, 1 fig., 4 tabs