Summary: Genome-wide association studies are now technically feasible and likely to become a fundamental tool in unraveling the ultimate genetic basis of complex traits. However, new statistical and computational methods need to be developed to extract the maximum information in a realistic computing time. Here we propose a new method for multiple association analysis via simulated annealing that allows for epistasis and any number of markers. It consists of finding the model with lowest Bayesian information criterion using simulated annealing. The data are described by means of a mixed model and new alternative models are proposed using a set of rules, e.g. new sites can be added (or deleted), or new epistatic interactions can be included between existing genetic factors. The method is illustrated with simulated and real data. © 2006 Oxford University Press.