Most complex diseases have not been amenable to genetic analysis under the assumption of single locus or multifactorial models. Consequently, interest has turned to the consideration of the properties of oligogenic models. i.e., genetic models involving a small number of genes. Nine two-locus models of disease, representing both epistatic and heterogeneous genetic models, are investigated: three models of heterogeneity and six models of epistatis. For each model we derive formulas for the recurrence risk to various classes of relatives in terms of penetrances and gene frequencies. We also develop formulas for the components of variance for the epistatic models in terms of the same genetic parameters. The range of penetrances and the associated gene frequencies that predict a predetermined value for the population prevalence and recurrence risk to the sibling of proband are calculated for various rates of the prevalence and risk to sibs. It is found that for many of these genetic models, there is a very limited range of penetrances that fit a particular set of assumed risks. Estimated population prevalence and risks to sibs and monozygotic twins for bipolar and schizophrenia illness are used to test for compatibility with expected values for recurrence risks under these models.