Statistical methods for mapping quantitative trait loci relative to genetic markers are now well established for continuous traits with normal distributions. However, many traits of economic importance are recorded on a discrete, ordinal scale. Here we describe a model developed for the analysis of ordinal traits, such as degree of difficulty in calving or categories of plant disease resistance. The model estimates the distance from the quantitative trait locus to neighbouring genetic markers, and also genetic parameters, either as gene effects on an underlying continuous scale or as probabilities of the observed categories. The model is tested on simulated data and is compared with an analysis based on mixtures of normal distributions. The ordinal model is found to estimate the parameters more accurately, especially when the number of categories is small or when only one linked marker is available.