The catalytic process, during which the catalyst loses activity, is usually difficult for investigation and industrial application, especially when the life time of the catalyst is relatively long (10 to 104 h). Therefore, experimental studies of the deactivation kinetics are very expensive, and mathematical modeling and simulation of the deactivation mechanisms becomes more significant, even more than models of reaction mechanisms. In this paper we present an approach to developing and analysis of deactivation dynamics models based on formalism of thermodynamics of non-equilibrium processes. The simplest two step sequence mechanism of the target reaction is used for deriving and analyzing models of reversible and irreversible deactivation mechanisms corresponding to poisoning and coking phenomena. Differential equations for dynamics of the key deactivation intermediate and of the target reaction rate, as well as of the catalyst relative activity are derived and solved. It is shown that thermodynamic formalism coupled with classic kinetic consideration is useful for the analysis of optimal bond energy of key intermediate with the catalyst, which can provide low deactivation.