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Genetic mapping of quantitative trait loci (QTLs) is performed typically by using a parametric approach, based on the assumption that the phenotype follows a normal distribution. Many traits of interest, however, are not normally distributed. In this paper, we present a nonparametric approach to QTL mapping applicable to any phenotypic distribution. The method is based on a statistic ZW, which generalizes the nonparametric Wilcoxon rank-sum test to the situation of whole-genome search by interval mapping. We determine the appropriate significance level for the statistic ZW, by showing that its asymptotic null distribution follows an Ornstein-Uhlenbeck process. These results provide a robust, distribution-free method for mapping QTLs.