Studying global mass balances and how they interact with the shape of column profiles, Dorn and Morari (Dorn, C.; Morari, M. Ind. Eng. Chem. Res. 2002, 41, XXXX) developed a graphical method for a qualitative stability analysis of steady-state profiles in homogeneous azeotropic distillation columns. Based on the qualitative stability analysis, here it is shown how bifurcation diagrams can be constructed containing information on the stability of the equilibria. Fold, Hopf, and homoclinic bifurcations as well as more complex bifurcations can be predicted. The existence of limit cycles is explained and their approximate shape determined. It is explained how the feed composition and the reflux flow rate influence the bifurcation behavior of the column. The results are compiled in two-parameter bifurcation diagrams as well as in projections of a three-parameter bifurcation diagram. The method is applied to predict several new phenomena in distillation, e.g., operating conditions for which the only steady state of the column is unstable and surrounded by a stable limit cycle. All predicted phenomena are confirmed by steady-state and dynamic simulations.