The steady-state simulation of a cocurrently cooled autothermal fixed-bed reactor was carried out using a 2-D heterogeneous mathematical model. The ammonia synthesis was chosen as a case study. Unlike the not-autothermal cocurrent reactor, which is unconditionally stable, the autothermal cocurrent reactor shows multiple steady states within a broad range of operating conditions. This finding, not reported in the literature, is explained through the mass transport from the bottom to the top of the reactor, associated with a feedback of energy. The feedback of heat, which is inherent to autothermal reactors, leads to an ignition-extinction phenomenon similar to that found in the countercurrent configuration. The influence of different parameters on the stability of the autothermal cocurrent reactor was analyzed. The regions where steady-state multiplicity occurs were compared with those presented by the autothermal countercurrent reactor The influence of an additional heat exchanger on the reactor stability was considered.