Historically, most methods for detecting linkage disequilibrium were designed for use with diallelic marker loci, for which the analysis is straightforward. With the advent of polymorphic markers with many alleles, the normal approach to their analysis has been either to extend the methodology for two-allele systems (leading to an increase in df and to a corresponding loss of power) or to select the allele believed to be associated and then collapse the other alleles, reducing, in a biased way, the locus to a diallelic system. I propose a likelihood-based approach to testing for linkage disequilibrium, an approach that becomes more conservative as the number of alleles increases, and as the number of markers considered jointly increases in a multipoint test for linkage disequilibrium, while maintaining high power. Properties of this method for detecting associations and fine mapping the location of disease traits are investigated. It is found to be, in general, more powerful than conventional methods, and it provides a tractable framework for the fine mapping of new disease loci. Application to the cystic fibrosis data of Kerem et al, is included to illustrate the method.