Flash and distillation systems evolving on the equilibrium manifold possess stable steady states when the molar flows and the boundary conditions are fixed and a vapor and liquid phase is present at all times. The results extend the range of validity of a local stability theorem for linear, constant molar overflow systems due to Acrivos and Amundson. The approach to stability analysis is motivated by the tangent plane method developed by Gibbs to open systems as it takes advantage of the negative curvature of the entropy surface to construct a Lyapunov function. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 3322-3332, 2013