The superorder Paracanthopterygii comprises five orders, four found in Australia and the fifth restricted to fresh waters of North America. Relationships and definition of the group are controversial and the group may not be monophyletic (Nelson 1994). Based on molecular work, Miya et al. (2005) proposed a very different classification including the transfer of Batrachoidiformes, Ophidiiformes and Lophiiformes to the Paracanthopterygii and Zeiformes to the Paracanthopterygii. We follow Nelson (2006) here in retaining the older classification pending further studies.
Miya, M., Satoh, T.P. & Nishida, M. 2005. The phylogenetic position of toadfishes (order Batrachoidiformes) in the higher ray-finned fish as inferred from partitioned Bayesian analysis of 102 whole mitochondrial genome sequences. Biological Journal of the Linnean Society of London 85(3): 289-306
Nelson, J.S. 1994. Fishes of the World. New York : John Wiley & Sons 600 pp.
Nelson, J.S. 2006. Fishes of the World. Hoboken, New Jersey : John Wiley & Sons, Inc. 601 pp.