The aim of the Joint Report of the two French Academies is to discuss the validity of the linear non threshold dose-effect relationship (LNT) for assessing the detrimental effects of small doses such as those delivered by X-ray examinations (0.1 mGy to 20 mGy). The conclusion of the report is that extrapolation with LNT could greatly overestimate those risks and thus may have a detrimental effect for public health by discouraging physicians and patients from performing potentially useful radiological examinations (for example a mammography or a CT scan) when the risk appears to be too large. This conclusion against the validity of LNT is based on several types of data: 1 Epidemiology has not evidenced cancer excess in humans for doses below 100 mSv. 2 Experimental animal data have not evidenced a carcinogenic effect for doses below 100 mSv. Moreover, dose-effect relationships are very seldom linear; most of them are linear-quadratic or quadratic. A practical threshold or hormetic effects have been observed in a large number of experimental studies. 3 Radiobiology: LNT assumes that the genotoxic risk (per unit dose) is constant irrespective of dose and dose rate and thus that the efficacy of the two guardians of the genome, DNA repair and elimination by death of cells with DNA damage do not vary with dose and dose rate. This assumption is not consistent with a large number of recent radiobiological data, for example mutational effect and lethal effect vary (per unit dose). The second assumption is that a given DNA damage has the same probability of initiating a cancer irrespective of the number of other DNA damage in the same cell and in the neighbouring cells. This assumption is also non consistent with recent data and modern concepts of carcinogenesis in which the microenvironment and tissue disorganisation play an important role. The existence of a threshold dose in individuals or animals contaminated by radium or thorium shows that the irradiation of a cell surrounded by non-irradiated cells does not initiate carcinogenesis. It is the responsibility of the proponents of LNT to demonstrate the validity of these two assumptions in order to justify the use of LNT. The recent reports do not provide such demonstrations. Copyright © 2006 Inderscience Enterprises Ltd.