As the result of-disruptions in the technological regimes or changes in the composition of the feed stock an uncontrollable increase of the temperature in catalyst pellets, which can lead to their sintering or destruction, is often observed. One of the primary reasons for gross overheating of catalyst pellet can be a transition from one steady state to another. The fundamental catalytic processes in the petrochemical-and chemical industries are characterized by a multistage set of the specific chemical transformations with a significant chemical transformations with a significant number of the reactants participating therein. One result is complications of the mathematical model of catalyst pellet, into with a large number of equations, beginning with heat and material balances, enter. This has led in many practical situations to extremely complicated procedures for analysis of steady-state multiplicity and to the impossibility of scientifically based selections of the mathematical model for a catalytic process, reflecting the results of industrial experimentation over a wide range of variation of the technological parameters. These difficulties can be successful overcome if the dimensionality of the model equations is sharply curtailed by the use of invariants of the physicochemical systems which are derived a priori.