We present a Bayesian approach to the problem of inferring the history of inversions separating homologous chromosomes from two different species. The method is based on Markov Chain Monte Carlo (MCMC) and takes full advantage of all the information from marker order. We apply the method both to simulated data and to two real data sets. For the simulated data, we show that the MCMC method provides accurate estimates of the true posterior distributions and in the analysis of the real data we show that the most likely number of inversions in some cases is considerably larger than estimates obtained based on the parsimony inferred number of inversions. Indeed, in the case of the Drosophila repleta-D. melanogaster comparison, the lower boundary of a 95% highest posterior density credible interval for the number of inversions is considerably larger than the most parsimonious number of inversions.