This study is aimed at improving the analysis of data used in identifying marker-associated effects on quantitative traits, specifically to account for possible departures from a Gaussian distribution of the trait data and to allow for asymmetry of marker effects attributable to phenotypic divergence between parental lines. A Bayesian procedure for analysing marker effects at the whole-genome level is presented. The procedure adopts a skewed t-distribution as a prior distribution of marker effects. The model with the skewed t-process includes Gaussian prior distributions, skewed Gaussian prior distributions and symmetric t-distributions as special cases. A Markov Chain Monte Carlo algorithm for obtaining marginal posterior distributions of the unknowns is also presented. The method was applied to a dataset on three traits (live weight, carcass length and backfat depth) measured in an F2 cross between Iberian and Landrace pigs. The distribution of marker effects was clearly asymmetric for carcass length and backfat depth, whereas it was symmetric for live weight. The t-distribution seems more appropriate for describing the distribution of marker effects on backfat depth.