Multiplicity of steady states can exist in three forms : input multiplicity, output multiplicity, and pseudo-multiplicity, which are described here. Input multiplicity is Likely to be common in reactive distillation and places substantial restrictions on the selection of controlled variables. Output multiplicity is also possible in reactive distillation and also has less significant implications for operation and control as it may influence the choices of control structure and the operating region. Pseudo-multiplicity parallels output multiplicity but is only present in terms of molar inputs. It has only minor implications for operation and control but is an important discovery as it reconciles recent reports of material balance output multiplicity with earlier conjecture which claimed that this was unlikely.