The recently released data on cancer incidence in the Japanese atomic bomb survivors are analysed using a variety of relative risk models which take account of errors in estimates of dose to assess the dose-response at low doses. For all solid cancers analysed together there is a significant positive dose-response (at the one-sided 2.5% significance level) if all survivors who received < 0.5 Sv are considered, but the significance vanishes if doses of < 0.2 Sv are considered. If a relative risk model with a threshold (the dose-response being assumed linear above the threshold) is fitted to the solid cancer data, a threshold of more than about 0.2 Sv is inconsistent with the data, whereas these data are consistent with there being no threshold. Linear-quadratic models and linear-quadratic models with an exponential cell-sterilization term provide no better fit than the linear model. For the three main radiation-inducible leukaemia subtypes analysed together (acute lymphatic leukaemia, acute myeloid leukaemia and chronic myeloid leukaemia) there is a significant positive dose-response (at the one-sided 2.5% significance level) if all survivors who received < 0.5 Sv are considered, but the significance vanishes if doses of < 0.2 Sv are considered. If a relative risk model with a threshold (the dose-response being assumed linear above the threshold) is fitted to the leukaemia data, a thresh-old of more than about 0.3 Sv is inconsistent with the data. In contrast with the solid cancer data, the best estimate for the threshold level in the leukaemia data is significantly different from zero, even when allowance is made for a possible quadratic term in the dose-response, albeit at borderline levels of statistical significance (p = 0.04). There is little evidence for curvature in the leukaemia dose-response from 0.2 Sv upwards. However, the possible underestimation of the errors in the estimates of the dose threshold as a result of confounding and uncertainties not taken into account in the analysis, together with the lack of biological plausibility of a threshold, makes the interpretation of this finding questionable.