After Nelson, 1994, with Recent species from Froese & Pauly, 2001 [“The Fishbase”]

<==o Anguilliformes Berg, 1940 (eels and relatives; ankeriaskalat)
   |--o Anguillavidae
   |  |--o †Anguillavus L.Cret. SWAs
   |  |  |-- †A. bathshebae
   |  |  `-- †A. quadripinnis
   |  |-- †Enchelurus L.Cret. Eu.
   |  |-- †Eoanguilla M.Eoc. Eu.
   |  `?- Mastygocerus Mioc.-R. EInd. [not regocnized by the Fishbase, Identifiacation and Recent status in Carroll (1988) highly suspecious]
   `--+--o †Urenchelys Woodward, 1900, L.Cret. Eu. NA. SWAs. [Urenchelyidae]
      |  |-- †U. avus Woodward, 1901
      |  |-- †U. abditus Wiley & Stewart, 1981
      |  |-- †U. anglicus Woodward, 1900
      |  |-- †U. germanus Hay, 1903
      |  `-- †U. hakelensis (Davis,1887)
      |-- Protoanguilla palau Johnson, Ida, Sakaue, Sado, Asahida & Miya, 2012 [Protoanguillidae Johnson, Ida, Sakaue, Sado, Asahida & Miya, 2012]
      `--+--o Anguilloidei (ankeriaansukuiset)
         |  |-- Anguillidae (freshwater eels; ankeriaat)
         |  |-- Heterenchelyidae
         |  `-- Moringuidae (worm eels; matoankeriaat)
         |?- Muraenoidei (Morey-like; mureenansukuiset)
         `--+-- Congroidei (conger-like; meriankeriaansukuiset)
            `-- Saccopharyngiformes (ahmattiankeriaskalat, pelikaanikalat)

Anguilliformes incertae sedis:

        †Gazolapodus M.Eoc. Eu.

    †Proteomyridae
        †Proteomyrus ventralis M.Eoc. Eu.

    †Milananguillidae
        †Milananguilla lehmani M.Eoc. Eu.

    †Patavichtidae
        †Patavichthys bolcensis M.Eoc. Eu.
        †Bolcanguilla brachycephala M.Eoc. Eu.

    †Paranguillidae
        †Dalpiazella brevicauda M.Eoc. Eu.
        †Paranguilla tigrina M.Eoc. Eu. 

    †Anguilloididae
        †Anguilloides M.Eoc.-Mioc. Eu.
        †A. branchiostegalis
        †Veronanguilla ruffoi M.Eoc. Eu.

After Johnson, Ida, Sakaue, Sado, Asahida & Miya, 2012

<==o Anguilliformes
   |-- Protoanguilla
   `--+-- Synaphobranchidae
      `--+--+-- Heterenchelyidae
         |  `--+-- Myrocongridae
         |     `-- Muraenidae
         `--+--+-- Moringuidae
            |  `--+--o Saccopharyngiformes
            |     |  |--+-- Eurypharyngidae
            |     |  |  `-- Saccopharyngidae
            |     |  `--+-- Monognathidae
            |     |     `-- Cyematidae
            |     `--+-- Nemichthyidae
            |        `--+-- Serrivomeridae
            |           `-- Anguillidae
            `--+-- Chlopsidae
               `--+--+-- Colocongridae
                  |  `-- Derichthyidae
                  `--+--+-- Conger [Congrinae]
                     |  `-- Nettastomatidae
                     `--+--+-- Ariosoma [Congrinae]
                        |  `--+-- Heterocongrinae
                        |     `-- Bathymurinae
                        `--+-- Ophichthyidae
                           `-- Mureanesocidae

Reference(s):