Genomic evidence is increasingly underpinning that hybridization between taxa is commonplace, challenging our views on the mechanisms that maintain their boundaries. Here, we focus on seven catadromous eel species (genus Anguilla) and use genome-wide sequence data from more than 450 individuals sampled across the tropical Indo-Pacific, morphological information, and three newly assembled draft genomes to compare contemporary patterns of hybridization with signatures of past introgression across a time-calibrated phylogeny. We show that the seven species have remained distinct for up to 10 million years and find that the current frequencies of hybridization across species pairs contrast with genomic signatures of past introgression. Based on near-complete asymmetry in the directionality of hybridization and decreasing frequencies of later-generation hybrids, we suggest cytonuclear incompatibilities, hybrid breakdown, and purifying selection as mechanisms that can support species cohesion even when hybridization has been pervasive throughout the evolutionary history of clades.