Can A Hermaphrodite Produce Sperm And Eggs?

Can A Hermaphrodite Produce Sperm And Eggs? Hermaphrodites can either reproduce by virtue of self-fertilization or they can mate with a male and use the male derived sperm to fertilize their eggs. While virtually the entire progeny that is produced by self-fertilization is hermaphroditic, half of the cross-progeny is male. Can a hermaphrodite self reproduce?