Polyazeotropy in binary systems is a very singular case of vapor-liquid equilibrium (VLE), and its causes have not been studied in detail. The unique evidence about the phenomenon is the experimental VLE results for the benzene-hexafluorobenzene system, which exhibits two simultaneous azeotropes. The purpose of this work is to make a thermodynamical analysis of polyazeotropy at low pressures and to establish the necessary and sufficient conditions that provoke it. The evolution of polyazeotropes with temperature and pressure is explained, and the criteria to predict azeotropic behavior from minimal information are developed. This study also delivers some important results about the possibility of predicting polyazeotropy using classical G̃E models and about estimation of the parameters for excess energy models from activity coefficients at infinite dilution, in particular, when this procedure generates changes of concavity for the G̃E function.