Due to the tightening requirements for environmental safety, N2O and H2O2 fuels have recently been attracting more attention as environmentally friendly ("green") types of fuel and, at the same time, high-energy monofuels in the field of space technology. The use of N2O and H2O2 makes it possible to implement new design solutions when creating a propulsion system for a spacecraft. However, their use is currently limited due to the lack of highly efficient decomposition catalysts. This paper presents the results of studying the relationship between the catalytic and thermodynamic properties of substances based on the applicability of the Bronsted-Temkin relation to the elementary stages of the catalytic reaction. The material analyzed in the paper illustrates this relationship in terms of the problem of choosing the optimal catalyst and the problem of predicting the reactivity of molecules. The paper presents the results of studying the regularities and mechanisms of the heterogeneous catalytic decomposition of nitrous oxide and hydrogen peroxide. It is shown that the presented mechanisms are mainly determined by the nature of oxygen participation in the intermediate chemical interaction during catalysis. For each of the considered processes, there are conditions under which atomic anions of adsorbed oxygen (O), which are similar in nature to diamagnetic ions of O-2 solid oxides, participate in the reaction. These particles appear either by adsorption of oxygen molecules (or atoms) or by interaction with the surface of unstable oxygen-containing molecules such as N2O and H2O2. The nature of activation of the oxidized molecules on the catalysts of various chemical natures has a significant influence on the mechanism of the considered reactions. The results of experimental studies presented in the paper and their analysis make it possible to develop a scientific approach to the selection of effective catalysts for the decomposition of N2O and H2O2.