Residue-curve and distillation-line maps are useful tools for the design of azeotropic distillation sequences. The calculation of residue curves uses the assumption that the vapour and liquid are always in equilibrium. The computation of distillation lines assumes that the vapour and liquid leaving a tray are in equilibrium. In this work, the equations defining residue curves and distillation lines are extended to take into account mass transfer effects that occur in real distillation columns. A general relationship between the composition of the vapour and liquid leaving a tray at total reflux is developed and used to calculate the maps. The curvature of the residue curves and distillation lines changes, significantly affecting the shape of the maps. The consideration of mass transfer in azeotropic distillation columns produces quantitative changes in the behaviour of the liquid composition path for distillation columns at total reflux, and in some cases, a qualitative change in the products formed can also be observed. No change has been found in the bounds on the product composition at minimum reflux when mass transfer effects are taken into account. The pinch-point curves or distillation limits remain the same. Entrainers should be selected considering not only how much they modify the vapour-liquid equilibrium, but also how much they affect the multicomponent mass transfer that takes place in real distillation columns.