For solutions of a mixture of two electrolytes with a common ion, the characteristic free energy function is ΔmGex, the change in excess free energy on forming the solution from solutions of the single electrolytes. This is closely related to Δm, where is the cluster integral sum of the Mayer theory. For systems that conform to Harned's rule the contributions of most of the cluster integrals to Δm are negligible. The form of the principle contribution to Δm depends on whether the two electrolytes have the same charge type (symmetrical mixtures) or not. The equations for symmetrical mixtures which nearly conform to Harned's rule are developed in detail, first for the general case in which the components of the potential of average force are arbitrary and then for the special case of hard sphere ions, designated as the primitive model for electrolyte solutions. The leading term of Δm is determined by the difference in short-range interaction of pairs of ions of the same charge and does not depend at all on the common ion. Another general result is that ΔmGex/I 2 does not vanish as I→0, as has sometimes been expected on the basis of the Brønsted principle of specific ion interaction, but approaches a finite value in a way that is governed by a higher-order limiting law. Comparison with experiment is made on the basis of the primitive model. The results are roughly consistent with the free energy effects in alkali metal chloride mixtures if it is assumed that the effective radii of the alkali metal ions are about double their crystal radii.