Coalescent theory, which describes the genealogical relationships among a group of genes as a function of population demography, can be used to make inferences on past population dynamics. The theoretical background provided by the coalescent describes the distribution of mutations among the sample of genes under different demographic scenarios. However, the actual number of mutations can rarely be deduced from DNA polymorphisms. The inclusion of mutation models in theoretical predictions can improve the performance of statistical methods. We have developed a maximum likelihood estimator for the parameters that characterize a demographic expansion for a series of linked loci evolving under a stepwise mutation model. That would correspond to DNA polymorphisms of linked microsatellites (such as those found on the Y-chromosome or the chloroplast genome). In a previous work, it was shown that linked microsatellites were sensitive to population expansions but that estimators based on number of mutations produced underestimation of the time of the expansion. We applied the new method to simulated data obtaining better estimates for the time of expansion.