The literature about product boundaries of homogeneous azeotropic distillation has been reviewed. A method for the calculation of multicomponent distillation from stage to stage has been developed. The method is based on balances around the product end of the cascade of equilibrium stages and iterates only the amount of the stream entering the cascade. By way of linearization of the method for the calculation of multicomponent distillation from stage to stage at a pinch point, a method for the calculation of separatrixes of distillation has been developed, which has already been utilized in a method for calculating minimum reflux of real multicomponent distillation (Poellmann et al. Comput Chem Eng (1994) 18 S49). The separatrixes of closed multicomponent distillation are identical with the product boundaries of closed multicomponent distillation. A separatrix of open distillation yields only one point of a product boundary of open distillation-its product. A method based on eigenvalue theory has been developed, which makes it possible to judge with respect to a pinch point whether the calculation of multicomponent distillation from stage to stage initiated at the product has the potential to leave the pinch point. If the pinch point is located on the boundary of the mole fraction space and if the calculation has the potential to leave this boundary, then the product can be reached by distillation of mixtures taken out of the interior of the multicomponent mole fraction space using infinitely many stages. The profile of reversible multicomponent distillation has been interpreted as a curve in mole fraction space with the temperature as parameter. A system of linear equations for the derivative of the profile of reversible multicomponent distillation with respect to the temperature has been given. Numerical integration of this derivative initiated at a point located on the desired profile yields the profile quickly and accurately even if the profile exhibits sharp corners. Even if two parts of a profile approach each other very closely, the numerical integration does not jump onto another part. The inflection points of residue curves have been identified as the bifurcation points of profiles of reversible ternary distillation. The envelope of the tangents to residue curves in their inflection points (Wahnschafft et al. Ind Eng Chem Res (1992) 31 2345) could be confirmed as the product boundary of reversible ternary distillation. A zero of the determinant of the matrix of coefficients of the system of linear equations for the calculation of the derivative of the profile of reversible multicomponent distillation with respect to the temperature has been developed as a necessary condition for a bifurcation of a profile of reversible multicomponent distillation. Sufficient for a bifurcation and thus a point of the product boundary of reversible ternary distillation on an inflection point tangent is the zero of the determinant, if the determinant is evaluated for the inflection point and for potential products on the tangent. Using the above-mentioned eigenvalue-based method, it could be shown that product which can be reached by reversible multicomponent distillation can also be reached by adiabatic open multicomponent distillation.