It is now well known that a supersaturated phase contains clusters, aggregates, or embryos of atoms, molecules, or ions. The many kinetic models of homogeneous nucleation generally refer to the equilibrium states of these supersaturated systems. In this paper, a thermodynamic model inspired by Prigogine and Defay's “associated solutions model” allows one to work out the Gibbs free energy of a supersaturated liquid solution and to make more precise essential notions such as critical nucleus and stability. At the same time, a new step-by-step description of the nucleation process is proposed. Lastly, a few experimental results concerning the precipitation of potassium sulfate from its supersaturated aqueous solutions are presented and the influence on the kinetics of precipitation of thermal treatments of the liquid phase is interpreted. References