The occurrence of gynodioecy among angiosperms appears to be associated with self-compatibility. We use individual-based simulations to investigate the conditions for breakdown of a gametophytic self-incompatibility system in gynodioecious populations and make a comparison with hermaphroditic populations where the conditions are well known. We study three types of mutations causing self-compatibility. We track the fate of these mutations in both gynodioecious and hermaphroditic populations, where we vary the number of S-alleles, inbreeding depression and selfing rate. We find that the conditions for breakdown are less stringent if the population is gynodioecious and that the breakdown of self-incompatibility tends to promote stability of gynodioecious populations since it results in a higher frequency of females. We also find that fecundity selection has a large effect on the probability of breakdown of self-incompatibility, in particular if caused by a mutation destroying the female function of the S-locus.