Steady state multiplicity in a single section of a distillation column involving ternary, homogeneous azeotropic mixtures is investigated. Multiple eigenvalues of the equilibrium relation are conjectured to be a potential source for steady state multiplicity. Continuation methods for large sparse systems are applied to determine operating conditions with multiple steady state solutions. An interpretation is given in terms of nonlinear wave propagation theory. Similar phenomena are shown to rise in a distillation column.