Simulation studies suggest that reactive distillation processes exhibit complex multiple steady state behavior in many cases, while sources for these multiplicities have not yet been identified adequately. A singularity theory approach is applied to one-stage reactive distillation columns to contribute to the identification of possible sources of steady state multiplicities especially those related to different chemical reactions. A proposed computational approach is characterized by requiring no analytical solution but still being mathematically rigorous. The highest-order singularity in the hierarchy of singularities is identified using computational interval methods. Results on esterifications and the ethylene glycol reaction in reactive distillation processes are presented. Reasons for multiplicities also common to non-reactive distillation processes as well as reasons directly connected to the interaction of chemical reaction and phase equilibrium are identified.