A system of excess functions is developed for electrolyte solutions and other solutions with an essentially unsymmetrical solvent-solute relation. These new functions vanish for a solution whose practical (molal scale) osmotic coefficient is unity at all compositions, temperatures and pressures. The use of these excess functions offers some advantages over other methods of comparing Mayer's ionic solution theory with experiment, of representing the properties of solutions of single or mixed electrolytes, and of making qualitative interpretations of the molecular basis of thermodynamic properties. Graphs showing the ionic-strength dependence of the excess free energy, excess enthalpy, excess entropy, and excess volume are given for several aqueous solutions of single electrolytes up to 6 molal. Experimental values of the cluster integral sum, the characteristic function of the Mayer theory, have also been calculated. The concentration dependence of this function is very similar to that of the excess free energy.