This paper reports studies on the bifurcation analysis and the generation of regions of multiplicity in the operation of moving-bed reactors. The studies were first carried out for a generalized model, which allows the investigation of the effect of various scenarios, such as changes in heat capacity or the number of moles with reaction, as well as the previously unstudied equilibrium and allothermic reactions. The insights gained from this extension were then applied to an actual reaction, namely the high temperature pyrolysis of methane.