The paper addresses control of distillation columns at open-loop unstable operating points. The fact that ideal two-product distillation columns may have right half plane poles has only recently been recognized. The paper provides evidence for the observed instability. It is shown that the columns may be stabilized by use of one-point control, i.e., feedback control of a composition or a temperature inside tile column. Finally, the impact of the right half plane pole on achieveable control performance is discussed.