Teleost fishes share a duplication of their entire genomes. We report here on a computational survey of structured non-coding RNAs (ncRNAs) in teleost genomes, focusing on the fate of fish-specific duplicates. As in other metazoan groups, we find evidence of a large number (11,543) of structured RNAs, most of which (~86%) are clade-specific or evolve so fast that their tetrapod homologs cannot be detected. In surprising contrast to protein-coding genes, the fish-specific genome duplication did not lead to a large number of paralogous ncRNAs: only 188 candidates, mostly microRNAs, appear in a larger copy number in teleosts than in tetrapods, suggesting that large-scale gene duplications do not play a major role in the expansion of the vertebrate ncRNA inventory.