Study of very closely linked DNA variants at various loci has frequently shown linkage disequilibrium. We studied three closely linked RFLPs at the apolipoprotein AI-CIII locus. Two variants detected by MspI and SstI were in strong linkage disequilibrium; but when conventional statistical tests were used, a third variant (PstI), located between the MspI and SstI markers, appeared to be in linkage equilibrium with these two" outside" markers. Similar discrepancies from the expected monotone relationship between physical distance and linkage disequilibrium have been reported by others. To investigate these discrepancies, the power to detect linkage disequilibrium was calculated. It could be shown that, for the gene frequencies encountered, very large sample sizes would be required to demonstrate negative (ie, repulsion-phase) linkage disequilibrium. Such numbers are usually very difficult to attain in human studies. Failure to demonstrate linkage disequilibrium by conventional methods therefore does not imply its absence. Appropriate nomograms and tables are provided.