The steady-state behavior of one-stage reactive distillation processes is analyzed, for an exothermic isomerization reaction with first-order kinetics and a light-boiling reactant. The dimensionless model distinguishes between state variables, control parameters, and system properties. Combination of state multiplicity and feasibility boundaries corresponding to total reflux or total reboil leads to complex steady-state behavior. Singularity theory is used to divide the Damkohler number-heat input space into regions with qualitatively different behaviors. Forty-five bifurcation diagrams are presented, exhibiting a maximum of three steady states, five feasibility boundaries, and three disconnected solution branches.