Order Anguilliformes - True Eels

Hagfish

Anguillidae
Freshwater Eels
False Moray

Chlopsidae
False Morays
Lamprey

Colocongridae
Short-tail Eels
Conger and Garden eels

Congridae
Conger and Garden Eels
Chimaeras

Cyematidae
Bobtail Snipe Eels
Bichirs

Derichthyidae
Longneck eels
Lamprey

Eurypharyngidae
Pelican Eel
Mud Eels

Heterenchelyidae
Mud Eels
Chimaeras

Monognathidae
Onejaws
Moringuidae

Moringuidae
Worm & Spaghetti Eels
Pike Congers

Muraenesocidae
Pike Congers
Moray Eels

Muraenidae
Moray Eels
Chimaeras

Myrocongridae
Atlantic Red Eels
Bichirs

Nemichthyidae
Snipe Eels
Lamprey

Nettastomatidae
Duckbill Eels
Two Band Clownfish

Ophichthidae
Snake Eels
Protoanguillids

Protanguillidae
Protoanguillids
Lamprey

Saccopharyngidae
Gulped Eels
Sawtooth Eels

Serrivomeridae
Sawtooth Eels
Cutthroat Eels

Synaphobranchidae
Cutthroat Eels

References:
Betancur-R, R., E. Wiley, N. Bailly, M. Miya, G. Lecointre, and G. Ortí. 2014. Phylogenetic Classification of Bony Fishes --Version 3 (http://www.deepfin.org/Classification_v3.htm)
Eschmeyer, W. N. (ed). Catalog of Fishes Classification (http://www.calacademy.org/scientists/catalog-of-fishes-classification/). Electronic version accessed 11 Nov 2014
Froese, R. and D. Pauly. Editors. 2014. FishBase. World Wide Web electronic publication. www.fishbase.org, version (08/2014).