As recently recognized, distillation columns, operating with reflux and boilup as independent inputs, may have multiple steady-state solutions, even in the ideal binary case. Two fundamentally different sources may cause the multiplicity, and in both cases some operating points are found to be unstable. This article provides evidence for the instability and discusses the effect of operating conditions on stability. Increasing the internal flow rates increases the probability of instability; when flows other than reflux and boilup are used as independent inputs, an operating point may become unstable if the level control is not sufficiently tight. In this case, a limit cycle, usually stable, appears as the steady state goes unstable.