Recently, the risk associated with low doses of ionizing radiation has gained new interest. Here, we analyze and discuss the major differences between two reports recently published on this issue; the report of the French Academy of Sciences and of the French Academy of Medicine published in March 2005, and the BEIR VII-Phase 2 Report of the American National Academy of Sciences published as a preliminary version in July 2005. The conclusion of the French Report is that the linear no-threshold relationship (LNT) may greatly overestimate the carcinogenic effect of low doses (<100 mSv) and even more that of very low doses (<10 mSv), such as those delivered during X-ray examinations. Conversely, the conclusion of the BEIR VII report is that LNT should be used for assessing the detrimental effects of these low and very low doses. The causes of these diverging conclusions should be carefully examined. They seem to be mostly associated with the interpretation of recent biological data. The point of view of the French Report is that these recent data are incompatible with the postulate on which LNT is implicitly based, namely the constancy of the carcinogenic effect per unit dose, irrespective of dose and dose rate.