Singularity theory is applied to a steady state heterogeneous fixed-bed reactor model in which backconduction of heat through the catalyst is assumed. A maximum of five solutions exist when either adiabatic or Danckwerts’ boundary conditions are assumed for the catalyst temperature although heat loss at the bed inlet increases the exothermicity of the reaction required for five solutions to exist. An empirical uniqueness criteria for this model, based on the zero and infinite solid phase conductivity limiting cases, is presented.