Generalized estimating equations (GEEs) (Liang and Zeger, 1986, Biometrika 73, 13-22) are used to fit genetic models to binary disease data for families of subjects in case-control studies. The GEEs include model specification of both the disease probabilities and the two-way (and possibly three-way) correlation coefficients of the family disease data. These quantities are modelled as nonlinear functions of unobserved genotypes, observed environmental covariates, and the unknown parameters; the functions reflect the method used to ascertain the family data. Goodness of fit is tested by allowing more flexible forms for the correlation coefficients, regressing them against covariates specific to the relevant pair (or triple) of family members. The approach is applied to family data obtained from simulated and real case-control studies. This semiparametric approach is less dependent on unverifiable assumptions and more computationally tractable than other methods for segregation analysis.