The assessment of the low temperature phase stability of alloy phases-substantially below 0degreesC-is not only of acedemic interest but also of considerable practical importance. However, attempts are rarely made to assess phase boundaries as they continue down towards the absolute zero temperature. The purpose of this work is to consider some specific aspects of phase stability, phase boundaries, and the related phase diagrams at low temperatures, in the light of the restrictions imposed by the Third Law we give a brief overview of its place within Thermodynamics. We point out that for ordinary materials the equilibrium state of 0 K simultaneously satisfies the two conditions that its energy and entropy are at their lowest possible values as permitted by the evolutionary constraints imposed on their state variables. Also, free internal state variables (such as the equilibrium compositions of coexisting phases) must be such that the rates of change of their equilibrium values as a function of temperature are zero at 0 K. The phase stability at low temperatures of several binary alloy systems are discussed within the above scheme (Cu-Ni, Cu-Zn, Pu-Ga, In-Sn, Metal-Hydrogen), with the general conclusion that while the Third Law rules out certain configurations of the phase diagram it cannot uniquely determine what the low temperature equilibrium-under the given conditions-must be. For example, the equilibrium state of 0 K of an ordinary crystalline material for which the configurational atomic arrangement is unconstrained, is always perfectly ordered, and the energy of any other configurational state, including the fully disordered state, must always be higher. This analysis is particularly important in connection with the long-term aging properties observed in some Pu-Ga alloys. (C) 2003 Elsevier Ltd. All rights reserved.