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γ‐irradiation of ethylene–propylene diene monomer (EPDM) elastomers under oxidant atmosphere was carried out in order to change their mechanical and dielectric behaviour. Three different formulations of EPDM (70 wt% ethylene, 28 wt% propylene; diene monomer: 2 wt% norbornene) were studied: a non‐crosslinked EPDM terpolymer, a crosslinked EPDM and a crosslinked EPDM stabilized with an antioxidant. Dielectric and mechanical relaxation show a β‐sub‐glass relaxation at about −120 °C (1 Hz) and an α‐relaxation at −15 °C (1 Hz) associated with the glass transition but influenced by the effects of irradiation. The local mobility associated with the β‐relaxation is only weakly influenced by γ‐irradiation up to 450 kGy. The α‐process is shifted to higher temperatures as a result of crosslinking and changes in the semicrystalline structure. The amplitude of the dielectric α‐process increases as a result of the formation of oxidized species during irradiation under oxygen. In contrast, the mechanical α‐relaxation amplitude decreases as a result of physical and chemical cross‐linking. It was shown that the main factors that determine the crosslinking/chain scission balance are (1) the presence of oxygen together with the irradiation dose, (2) the dose rate and (3) the initial crosslink density of the EPDM material. As a result, the individual contribution of crosslinking and crystallization, and therefore the understanding and prediction of the properties after γ‐irradiation can only be deduced after comparison of the polymer behaviour below and above its melting temperature. Copyright © 2004 Society of Chemical Industry