Asexual populations are usually considered evolutionary dead-ends because they lack the mechanisms to generate and maintain sufficient genetic diversity. Yet, some asexual forms are remarkably widespread and genetically diverse. This raises the question whether asexual systems are always truly clonal or whether they have cryptic forms of sexuality that enhance their viability. In the planarian flatworm Schmidtea polychroa parthenogens are functional hermaphrodites (as are their sexual conspecifics), copulate and exchange sperm. Sperm is required for initiation of embryogenesis but usually does not contribute genetically to the offspring (sperm-dependent parthenogenesis). Using karyology and genotyping of parents and offspring, we show that in a purely parthenogenetic population an estimated 12% of all offspring are the result of partial genetic exchange. Several processes of chromosome addition and loss are involved. Some of these result in an alternation between a common triploid and a rare tetraploid state. We conclude that genetic recombination does not necessarily require segregation and fusion within the same generation, as is the case in most sexual species. These occasional sexual processes help to explain the geographical dominance of parthenogens in our study species.