The γ-radiolysis of fullerenes (C60 and C70) was performed to investigate the role of fullerenes as a carbon source in building organic molecules in astrophysical ice analog media. Mass spectrometric analyses and the sequential collision-induced dissociation processes enabled us to determine the plausible chemical structure of new products originated during γ-irradiation of fullerenes. The radiolytic products are grouped into six principal compound families. We assessed the relative yield, as percentage, for each new radiolytic compound, and designed the reaction schemes that lead to γ-irradiation products. The reactions start with the formation of primary radicals due to the radiolysis of solvents that react with the fullerenes' structures, forming fullerene radical adducts. The fate of these fullerene radical adducts depends on two factors: (i) the nature of radicals formed by irradiation of solvents and consequently by their ability to give secondary reactions, (ii) whether the onset of thermalization energy processes occurs or does not occur. Here, we present the results regarding the fragmentation processes that lead to functionalized carbonaceous chains characterized by lower molecular weight. We identify the chemical nature of functionalized chain products, propose the reaction schemes, and quantify their relative yields.