Abstract Given molecular genetic data from diploid individuals that, at present, reproduce mostly or exclusively asexually without recombination, an important problem in evolutionary biology is detecting evidence of past sexual reproduction (i.e., meiosis and mating) and recombination (both meiotic and mitotic). However, currently there is a lack of computational tools for carrying out such a study. In this article, we formulate a new problem of reconstructing diploid genealogies under the assumption of no sexual reproduction or recombination, with the ultimate goal being to devise genealogy-based tools for testing deviation from these assumptions. We first consider the infinite-sites model of mutation and develop linear-time algorithms to test the existence of an asexual diploid genealogy compatible with the infinite-sites model of mutation, and to construct one if it exists. In this ideal case, our chance of detecting signatures of past sexual reproduction is maximized. Then, we relax the infinite-sites assumption and develop an integer linear programming formulation to reconstruct asexual diploid genealogies with the minimum number of homoplasy (back or recurrent mutation) events. If this number is substantially larger than that expected for typical asexual organisms, then it may suggest that sexual reproduction or recombination may have played an important role in the evolutionary history. We apply our algorithms on simulated data sets with sizes of biological interest.