Automotive catalytic converters show highly transient operation due to fluctuating exhaust gas conditions in real application. Local ignition of the reactions with very steep temperature gradients as well as moving reaction fronts can occur in the monolithic catalyst. Theoretical investigations are presented based upon detailed simulation studies with a one-dimensional two-phase model for the catalytic converter. The simulation of the heat-up of the automotive catalyst during the cold-start shows a highly transient behavior for different cold-start concepts. Also, hot spot phenomena can be observed in the simulation under specific exhaust gas conditions.