The total vapour pressure of liquid mixtures of argon and krypton has been measured over the whole range of composition at 115.77°K (the triple-point of krypton) and at 103.94°K from an argon mole fraction of 0.4 to unity. The volume increase VE on mixing per mole has also been determined (at 115.77°K). The excess Gibbs energy GE of mixing per mole has been evaluated, and for a given mixture is only about half that estimated from earlier experimental studies of this system. For the equimolar solution, GE is 20.06 cal at 115.77°K, and 19.71 cal at 103.94°K. VE is negative, and has an unsymmetrical dependence on mole fraction. The experimental GE has been compared with values calculated from statistical theories of solutions. Theories based on the “two-liquid” or “refined average potential” model predict GE values too high by a factor of about 2. The calculated values are relatively little affected by the choice of intermolecular energy parameters or by the precise form of the intermolecular potential adopted. Values calculated on the “three-liquid” or “separate interaction” model are in much closer agreement with experiment. None of the ways of calculating VE at present available is satisfactory when applied to the argon + krypton system. A possible reason for the unsymmetrical variation of VE with composition is briefly considered. Details are given of a simple but efficient low-temperature fractionating column.