Bayesian posterior distributions are obtained for the time to the most recent common ancestor (MRCA) for a nonrecombining segment of DNA (such as the nonpseudoautosomal arm of the Y chromosome or the mitochondrial genome) for two individuals given that they match at k out of n scored markers. We argue that the distribution of the time t to the MRCA is the most natural measure of relatedness for such nonrecombining regions. Both an infinite-alleles (no recurring mutants) and stepwise mutation model are examined, and these agree well when n is moderate to large and k/n is close to one. As expected, the infinite alleles model underestimates t relative to the stepwise model. Using a modest number (20) of microsatellite markers is sufficient to obtain reasonably precise estimates of t for individuals separated by 200 or less generations. Hence, the multilocus haplotypes of two individuals can be used not only to date very deep ancestry but also rather recent ancestry as well. Finally, our results have forensic implications in that a complete match at all markers between a suspect and a sample excludes only a modest subset of the population unless a very large number of markers (>500 microsatellites) are used.