Using the sol-gel method, amine-curing polymer silica composites based on cycloaliphatic epoxy resin were obtained. The content of SiO2 filler in the composites was 0.5–10 wt %. The formed mass fractal of silica nanoparticles during the synthesis of composites has a reinforcing effect on the epoxy polymer matrix. The patterns of non-isothermal destruction of polymers and composites in the presence of atmospheric oxygen have been established. At 5 wt % SiO2, the effective activation energy of the main stage of destruction of composites increases from 165 to 254 kJ mol–1. As a result, the rate of weight loss of the samples decreases (the temperature corresponding to 50% weight loss shifts towards higher values by 30°C). The mechanism of high-temperature oxidation of pure polymer and composite with oxygen has been studied. It has been established that the introduction of SiO2 into the composition of composites increases the activation energy of isothermal oxidation of the substrate.