An electrolyte consisting of KBr or LiBr and Al2Br6 dissolved in toluene was studied. This is representative of a class of electrolytes consisting of an ionic bromide or iodide and aluminum bromide dissolved in an aromatic hydrocarbon or mixture of aromatic hydrocarbons, which can serve as a practical bath for the electroplating of aluminum on an industrial scale. The system is unique in that it combines a reasonably high electrolytic conductivity with a very low value of the dielectric constant of the solvent. The transference numbers were determined by two independent methods in an attempt to identify the predominant ionic species. Results based on measurements by the Hittorf method indicate that Al2Br7- is the basic ionic unit containing aluminum. All combinations containing AlBr4- lead to an unreasonable value for the sum of the transference numbers of the anion and the cation. Combining this with transference numbers determined by the emf method leads to the conclusion that the predominant ionic species in this system are [K2(Al2Br7)]+ and [K(Al2Br7)2]-. This conclusion is consistent with the well-known properties of the system, namely, that aluminum bromide exists as a dimer in solution in aromatic hydrocarbons, that the solubility of KBr (or LiBr) in the pure solvent is vanishingly small and its solubility in the present system is proportional to the concentration of Al2Br6, and that the conductivity of this electrolyte is unexpectedly high in view of the nonpolar nature of the solvent.