Elastomers are susceptible to chemical ageing, i.e., scission and cross-linking, at high temperatures. This thermally driven ageing process affects their mechanical properties and leads to limited operating time. Continuous and intermittent stress relaxation measurements were conducted on ethylene propylene diene rubber (EPDM) and hydrogenated nitrile butadiene rubber (HNBR) samples for different ageing times and an ageing temperature of 125 °C. The contributions of chain scission and cross-linking were analysed for both materials at different ageing states, elucidating the respective ageing mechanisms. Furthermore, compression set experiments were performed under various test conditions. Adopting the two-network model, compression set values were calculated and compared to the measured data. The additional effect of physical processes to scission and cross-linking during a long-term thermal exposure is quantified through the compression set analysis. The characteristic times relative to the degradation processes are also determined.