The dominant view of the phylogeny of living elasmobranchs, based on morphological characters, is that batoids (skates and rays) are derived sharks, joined with saw sharks, and angel sharks in the clade Hypnosqualea [S. Shirai, Squalean Phylogeny: A New Framework of 'Squaloid' Sharks and Related Taxa, Hokkaido University Press, Sapporo, 1992]. By contrast, a recent molecular-phylogenetic study based on mitochondrial genes for 12S and 16S rRNA and tRNA valine [C.J. Douady et al., Mol. Phylogenet. Evol., 26 (2003) 215-221] supported the older view that batoids and sharks are separate lineages. Here, we tested these two different views using combined, nuclear large-subunit and small-subunit rRNA gene sequences ( approximately 5.3kb) from 22 elasmobranchs, two chimeras, and two bony fishes. We used maximum likelihood, maximum parsimony, minimum evolution, and Bayesian inference for tree reconstruction, and found the large-subunit rRNA gene to contain far more signal than the small-subunit gene for resolving this mostly Mesozoic radiation. Our findings matched those of in separating batoids from sharks and in statistically rejecting Hypnosqualea. The angel shark (Squatina) was the sister group to squaliforms (dogfish sharks), and our findings are consistent with the idea that "orbitostylic" sharks form a monophyletic group (squaliforms+the hexanchiform Chlamydoselachus+Squatina+Pristiophorus). In the galeomorph sharks, however, lamniforms grouped with orectolobiforms, opposing the widely accepted 'lamniform+carcharhiniform' grouping. A tree based on the mitochondrial gene for cytochrome b also supported a separation of sharks and batoids, in contrast to Hypnosqualea. Among elasmobranchs, variation in the evolutionary rates of the nuclear rRNA genes was higher than that of cytochrome b genes, mainly due to the relatively rapid evolution of rRNA in some carcharhiniforms. In conclusion, several different molecular studies now refute the Hypnosqualea hypothesis of elasmobranch interrelationships.