Fundamentals and computer-aided methods of practice for the calculation and checking of azeotropes, and for the qualitative nd rigorous determination of separating spaces for closed distillation are presented, which are valid for non-ideal multicomponent systems. Separating spaces can occur in azeotropic systems only and are decisive for the separability of a system, if distillation is the separation technique. As a prerequisite, a rigorous mathematical model of the vapour-liquid equilibrium is required. The eigenvalues and eigen vectors of the Jacobian matrix of the equilibrium concentrations are the key ingredients of several methods: the eigenvalues describe the asymptotic behaviour of closed distillation profiles, which indicates the order according to which components can be separated; the eigenvalues enter a topological equation for checking the thermodynamic consistency of the azeotropes of a system; the eigenvectors initiate paths connecting azeotropes and pure substances, from the network of which separating spaces can be deduced qualitatively; and eigenvectors are essential to initiate the rigorous profiles of separating spaces.