To avoid problems related to unknown population substructure, association studies may be conducted in founder populations. In such populations, however, the relatedness among individuals may be considerable. Neglecting such correlations among individuals can lead to seriously spurious associations. Here, we propose a method for case-control association studies of binary traits that is suitable for any set of related individuals, provided that their genealogy is known. Although we focus here on large inbred pedigrees, this method may also be used in outbred populations for case-control studies in which some individuals are relatives. We base inference on a quasi-likelihood score (QLS) function and construct a QLS test for allelic association. This approach can be used even when the pedigree structure is far too complex to use an exact-likelihood calculation. We also present an alternative approach to this test, in which we use the known genealogy to derive a correction factor for the case-control association chi2 test. We perform analytical power calculations for each of the two tests by deriving their respective noncentrality parameters. The QLS test is more powerful than the corrected chi2 test in every situation considered. Indeed, under certain regularity conditions, the QLS test is asymptotically the locally most powerful test in a general class of linear tests that includes the corrected chi2 test. The two methods are used to test for associations between three asthma-associated phenotypes and 48 SNPs in 35 candidate genes in the Hutterites. We report a highly significant novel association (P=2.10-6) between atopy and an amino acid polymorphism in the P-selectin gene, detected with the QLS test and also, but less significantly (P=.0014), with the transmission/disequilibrium test.