Breast cancer-susceptibility genes BRCA1 and BRCA2 have recently been identified on the human genome. Women who carry a mutation of one of these genes have a greatly increased chance of developing breast and ovarian cancer, and they usually develop the disease at a much younger age, compared with normal individuals. Women can be tested to see whether they are carriers. A woman who undergoes genetic counseling before testing can be told the probabilities that she is a carrier, given her family history. In this paper we develop a model for evaluating the probabilities that a woman is a carrier of a mutation of BRCA1 and BRCA2, on the basis of her family history of breast and ovarian cancer in first- and second-degree relatives. Of special importance are the relationships of the family members with cancer, the ages at onset of the diseases, and the ages of family members who do not have the diseases. This information can be elicited during genetic counseling and prior to genetic testing. The carrier probabilities are obtained from Bayes's rule, by use of family history as the evidence and by use of the mutation prevalences as the prior distribution. In addressing an individual's carrier probabilities, we incorporate uncertainty about some of the key inputs of the model, such as the age-specific incidence of diseases and the overall prevalence of mutations. There is some evidence that other, undiscovered genes may be important in explaining familial breast cancer. Users of the current version of the model should be aware of this limitation. The methodology that we describe can be extended to more than two genes, should data become available about other genes.