Recent results from studies on the thermodynamics of mixing of aqueous solutions containing tetraalkylammonium halides have shown that these systems exhibit complex interactions (i.e. one or both solute components do not obey Harried's rule). We have found that in these complex mixtures, it is important to avoid models that assume Harried's rule is obeyed or that do not account for all multiplet interactions occurring in solution. The mixture parameters obtained from the Scatchard, Rush, and Johnson (SRJ) equations are compared to those obtained from the Scatchard, Rush, and Johnson equations modified by Leifer and Wigent (SRJ-LW) to show the importance of including all parameters associated with a given multiplet found in solution. Using the SRJ-LW equations along with the theory of co-spheres developed by Gurney and extended by Desnoyers and co-workers, the Reilly and Wood (RW) equations are shown to be unsuitable for systems which do not exhibit Harned rule behavior. It is desirable, particularly for chemical process simulations, to determine the excess free energy in terms of constants which are characteristic of the complex species formed. However, in complex mixtures, the concentrations of every complex species formed in a solution are required to determine these constants. In these complex systems where the individual species concentrations are not known, it is wise to draw only general conclusions regarding the species formed in solution. Using the SRJ-LW parameters, the excess free energy due to pair, triplet, and quadruplet interactions are reported and compared for the systems Pr4NBr-KBr-H2O, Pr4NCl-NaCl-H2O, Bu4NCl-NaCl-H2O, and Bu4NCl-LiCl-H2O. It will be shown that both the size of the clathrate ion and the hydrophilic nature of the accompanying cation have significant effects on the type and extent of complex species formed in aqueous solution. (C) 2003 Elsevier B.V. All rights reserved.