A new rigorous method For the determination of the minimum reflux and reboil ratios for nonideal homogeneous distillation is outlined. The method is based on column simulation with a large number of equilibrium stages to mimic an infinitely high column. The MESH equations are solved, when necessary, by a homotopy continuation method. Instead of product compositions, feasible keys are specified. The search strategy for the minimum ratios is based on the fact that the column pinches at the minimum internal recycle lead to a decoupling of the column ends. It is shown by several examples that the method can be applied to highly nonideal multicomponent mixtures. Until now, the need for manual iteration has been overcome. Even though the code is not properly speeded up, the execution time is promising with the current PC technology. Furthermore, some pitfalls in minimum energy calculations, which have been overlooked in the literature, are reported in this paper.