This paper addresses fundamental issues and models that have been used in the theory of nucleation in binary vapor systems. The meaning in thermodynamics of models is discussed, and three purely thermodynamic models are analyzed and compared. For the binary condensation nucleus, these are the capillarity model of classical nucleation theory, the modified capillarity model due to Renninger and Wilemski (RW), and the Gibbs model (usually referred to as the Gibbs theory). The Gibbs model is of course the most sophisticated and general, but its application requires more information than is available in macroscopic thermodynamic observables. Consistent thermodynamic analyses of the capillarity and RW models are performed and, for argon-krypton binary system, the two are compared with Monte Carlo simulation to assess which is the more accurate. Despite the genuinely inspired idea of the RW model, the classical model proves, by far, to be the most accurate. Finally, the extended modified liquid drop model, which is an augmentation of the classical capillarity model by an inclusion of statistical ideas such as fluctuations, is applied to the argon-krypton system. This model, which uses only macroscopic thermodynamic parameters and does not require knowledge of intermolecular potentials, predicts behavior that agrees remarkably well with the results of simulation. Its accuracy in this respect could be general enough to render it applicable to a large number of binary systems. In general the analysis in this paper makes use of fluids confined to a spherical container. This approach offers the great advantage of allowing the "nucleus" to be dealt with as a thermodynamically stable entity. (C) 2003 American Institute of Physics.