Cyclic distillation can bring new life in old distillation columns, by using a periodic operation mode that leads to significant benefits, such as: increased column throughput, lower energy requirements and much higher separation performance. The literature reveals experimental and theoretical studies carried out so far, including models for simulating cyclic distillation. However, the accuracy of these models is limited due to the assumption of linear thermodynamic vapor liquid equilibrium (VLE) and these models can be used only for rating studies. Moreover, no design method has been reported so far for the general case of multi-component mixtures and nonlinear equilibrium. This paper fills this gap by presenting a novel rigorous model, an intuitive graphical representation and an insightful comparison against conventional distillation. The design problem is formulated as a set of delay-differential equations with events and discontinuities. Several case studies involving ideal and non-ideal mixtures (e.g. benzene/toluene/o-xylene, methanol/water and ethanol/n-propanol separations) illustrate the process design and demonstrate the high flexibility and good controllability of cyclic distillation. (C) 2014 Elsevier B.V. All rights reserved.