Both Kohlrausch's law and the Debye–Hückel–Onsager equation break down as the concentration of the electrolyte increases above a certain value. The reason for this is that as concentration increases the average distance between cation and anion decreases, so that there is more interactions between close ions. Whether this constitutes ion association is a moot point. However, it has often been assumed that cation and anion interact to form an ion pair. So, an "ion-association" constant , can be derived for the association equilibrium between ions A and B:
: A + B  AB  with   = 
Davies describes the results of such calculations in great detail, but states that  should not necessarily be thought of as a true equilibrium constant, rather, the inclusion of an "ion-association" term is useful in extending the range of good agreement between theory and experimental conductivity data. Various attempts have been made to extend Onsager's treatment to more concentrated solutions.
The existence of a so-called conductance minimum in solvents having the relative permittivity under 60 has proved to be a controversial subject as regards interpretation. Fuoss and Kraus suggested that it is caused by the formation of ion triplets, and this suggestion has received some support recently.
Other developments on this topic have been done by Theodore Shedlovsky, E. Pitts, R. M. Fuoss, Fuoss and Shedlovsky, Fuoss and Onsager.