Abstract Ionising γ radiation produces reactive oxygen species by water radiolysis, providing an interesting model approach for studying oxidative stress in plants. Three‐week old plants of Arabidopsis thaliana were exposed to a low dose rate (25 mGy h −1 ) of γ radiation for up to 21 days. This treatment had no effect on plant growth and morphology, but it induced chronic oxidation of lipids which was associated with an accumulation of reactive carbonyl species (RCS). However, contrary to lipid peroxidation, lipid RCS accumulation was transient only, being maximal after 1 day of irradiation and decreasing back to the initial level during the subsequent days of continuous irradiation. This indicates the induction of a carbonyl‐metabolising process during chronic ionising radiation. Accordingly, the γ‐radiation treatment induced the expression of xenobiotic detoxification‐related genes ( AER , SDR1 , SDR3 , ALDH4 , and ANAC102 ). The transcriptomic response of some of those genes ( AER , SDR1 , and ANAC102 ) was deregulated in the tga256 mutant affected in three TGAII transcription factors, leading to enhanced and/or prolonged accumulation of RCS and to a marked inhibition of plant growth during irradiation compared to the wild type. These results show that Arabidopsis is able to acclimate to chronic oxidative stress and that this phenomenon requires activation of a carbonyl detoxification mechanism controlled by TGAII. This acclimation did not occur when plants were exposed to an acute γ radiation stress (100 Gy) which led to persistent accumulation of RCS and marked inhibition of plant growth. This study shows the role of secondary products of lipid peroxidation in the detrimental effects of reactive oxygen species.