Individuals carrying cancer-predisposing germline mutations are known to be at a higher risk for cancers than those who do not carry them. This is also true of their biological relatives because they have a higher probability of being carriers of such mutant genes than unrelated individuals in the population. Further, there are now sufficient grounds for assuming that cancer-predisposed individuals may also be at a higher risk for cancers induced by ionizing radiation. In our earlier work, we examined the impact of this heterogeneity (with respect to cancer predisposition and radiosensitivity differentials) on risks of radiation-induced cancer at the population level. This paper is focused on the question of risks of radiation-induced cancer in relatives of cancer-predisposed individuals. Using an autosomal dominant model of cancer predisposition and radiosensitivity developed earlier and applying it to breast cancer risks associated with mutations in the BRCA1 gene, we show that: (1) The risk ratio (i.e. the ratio of risk of radiation-induced cancer in relatives to that in unrelated individuals) in the population increases with the degree of biological relatedness of the relative, being higher for close than for distant relatives; incomplete penetrance of the mutant gene "dilutes" this risk ratio. (2) The proportion of excess radiation-induced cancers in relatives (i.e. the attributable fraction) is higher than in unrelated individuals. (3) In relatives, the proportion of excess cancers due to radiosensitivity differentials alone depends on the strength of predisposition, the radiosensitivity differentials assumed, the radiation dose, the proportion of cancers due to predisposition, the mutant gene frequency and the penetrance of the mutant gene. This is in contrast to the situation for unrelated individuals, for whom the above-mentioned proportion is dependent on the first three but not on the last three of these factors. Further, even when the proportion of excess cancers is small, most of it is due to radiosensitivity differential alone both in unrelated individuals and in relatives. (4) For values of predisposition strength and radiosensitivity differential <10, even when the estimated frequency of a mutant BRCA1 gene is 0.0047 and the proportion of breast cancers due to these mutations is 38% (as is the case for Ashkenazi Jewish women under age 30), the increase in breast cancer risks is only marginal even for first-degree relatives. (5) These findings support the conclusion that increases in radiation risks to relatives (compared to those in unrelated individuals), to be detectable epidemiologically, will occur only when the mutant alleles are common and the strength of predisposition and radiosensitivity differentials are conjointly dramatic.