The transmission/disequilibrium test (TDT) of Terwilliger and Ott [Hum Hered 1992;42:337-346] and Spielman et al. [Am J Hum Genet 1993;52:506-516] is widely used to detect linkage and/or association between a genetically influenced disease and the alleles of a codominant marker locus. The TDT was specifically designed to avoid the spurious population associations produced by ethnic stratification of a sample of affected people. In this paper, we describe permutation extensions of the TDT that share this advantage. Our conditional inference framework permits extensions to multiple alleles, multiple loci, unaffected siblings, and genotypic rather than allelic associations. In the case of multiple loci, the conditional perspective provides a straightforward correction for multiple tests that can be substantially more powerful than the standard Bonferroni correction.