Some general arguments based upon the behavior of correlation and thermodynamic functions near critical points leads us to expect that for some real electrolytes the interfacial excess ionic adsorption isotherms (even for co-ions) will have large maxima at temperatures and concentrations in the vicinity of a critical point of the electrolyte. Such predictions are beyond the scope of the Gouy-Chapman (GC) theory and most other theories of the double layer. The reason for the failure of these theories is pointed out. Some real systems which may exhibit this anomalous adsorption are given. © 1983 American Chemical Society.