The boiling point curves of binary liquid mixtures provide sufficient information leading to the characterization of the real-phase equilibrium behavior. The extremes of these curves indicate azeotropy. The topological consideration of all possible forms of boiling point curves in homogeneous binary systems suggests a new classification of vapor-liquid equilibrium (VLE) behavior. Rigorous thermodynamic relations are derived, whereby component vapor pressure P-i(s) and limiting activity coefficients gamma (infinity)(i) are required only to identify the azeotropic behavior of binary mixtures without the need of extensive measurements or calculations. The validity and the application of the derived conditions are proved by using experimental VLE, P-i(s), and gamma (infinity)(i) data.