The adaptive significance of female polyandry has become a recurrent subject of recent theoretical and empirical research. It has been argued that in addition to direct benefits, such as nuptial gifts or an adequate sperm supply, females may gain genetic benefits from mating with different males. Females of the scorpionfly Panorpa cognata mate with several males during their lifetime. In an experiment designed to rule out any direct nutritional benefit of multiple matings, I found that polyandrous females that mated with two different males achieved a significantly higher egg-hatching success than monandrous females that mated twice with the same male. However, individual males did not trigger the same response in different females as the egghatching success of different females that mated with one and same male did not correlate. The results, thus, do not conform to predictions from hypotheses assuming that genetic benefits of polyandry are influenced by the intrinsic genetic quality of males. The results are, however, consistent with the genetic incompatibility hypothesis. Nevertheless, substances from different males transferred during copulation may synergistically affect zygote viability. Furthermore, I discuss why paternity studies can only explicitly test the genetic incompatibility hypothesis if there are a priori expectations of female-male genome compatibilities.