The entire range of gas phase reaction products, depending on the composition of initial binary mixtures of methane and carbon dioxide in dielectric barrier discharges, has been determined (saturated as well as unsaturated hydrocarbons and oxygenated organic compounds). The macro-kinetics of the basic chemical pathways of the system under consideration has been investigated. This system is found to display a strong feedback effect (positive or negative, depending on the initial state of the surfaces, as well as the chemical composition of the feed-gas mixture). It is demonstrated that these properties undergo significant changes during operation, due to surface modification processes (polymer film deposition, its oxidation or reduction). They are found to exert a considerable influence on the chemical efficiency of the discharge (for example, on the absolute and relative chemical yields of the reaction products), the Lissajous figures appear to be a sensitive tool to monitor the operation conditions of the discharge.