The effect of the structure of promising antioxidant agents with prospective medical use, i.e., unsubstituted and para-substituted annelated triazinylacetic acid hydrazides, on their melting points, thermal stabilities, pyrolysis and oxidative decomposition stages and the type of volatiles emitted under heating with the use of DSC and TG/DTG/FTIR/QMS methods was evaluated and discussed. The melting point of the investigated compounds increased with an enhanced number of electrons (directly correlated with their molecular weight). Melting enthalpy values were determined and presented for all the studied compounds. The pyrolysis and oxidative decomposition processes of the analysed molecules consisted of several poorly separated stages, which indicated a multi-step course of the decomposition reactions. It was found that the thermal stability of the tested compounds depended on the type of substituent at the para position of the phenyl moiety or its absence. In both atmospheres used (air and helium), the thermal stability increased in relation to R as follows: -CH3 ≤ -OCH3 < -H < -OC2H5. In an inert atmosphere, it was higher by approx. 8–18 °C than in an oxidative atmosphere. The pyrolysis was connected with the emission of NH3, HCN, HNCO, HCONH2, HCHO, CO2, CO and H2O in the case of all the tested compounds, regardless of the substituent attached. In the case of the derivative containing the para-CH3 group, para-toluidine was an additional emitted aromatic product. In turn, emissions of aniline and alcohol (methanol or ethanol) for compounds with the para-OCH3 and para-OC2H5 groups, respectively, were confirmed. In oxidative conditions, the release of NH3, NO, HCN, HNCO, HCONH2, CO2, H2O and cyanogen (for all the compounds) and para-toluidine (for the para-CH3 derivative), aniline (for para-OCH3, para-OC2H5 and unsubstituted derivatives) and acetaldehyde (for the para-OC2H5 derivative) were clearly observed. No alcohol emissions were recorded for either compound containing the para-OCH3- or para-OC2H5-substitututed phenyl ring. These results confirmed that the pyrolysis and oxidative decomposition of the investigated annelated triazinylacetohydrazides occurred according to the radical mechanism. Moreover, in the presence of oxygen, the reactions of volatiles and residues with oxygen (oxidation) and the combustion process additionally proceeded.