The transmission-disequilibrium test (TDT) is a model-free method to detect linkage between a marker and a trait locus. Originally developed to map disease genes in human genetics, this statistic has been recently extended to deal with quantitative characters. The emphasis of current research is on investigating statistical properties of the test applied to data from livestock populations. For various constellations of sample parameters, it is shown via simulation that the empirically derived null hypothesis distribution of TDT remains in good agreement with its asymptotic distribution while its power is satisfactory only for very close linkage. TDT is then applied to a real data set from milk production data of a dairy cattle population.