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.

    †ProteomyridaeProteomyrus ventralis M.Eoc. Eu.

    †MilananguillidaeMilananguilla lehmani M.Eoc. Eu.

    †PatavichtidaePatavichthys bolcensis M.Eoc. Eu.
        †Bolcanguilla brachycephala M.Eoc. Eu.

    †ParanguillidaeDalpiazella brevicauda M.Eoc. Eu.
        †Paranguilla tigrina M.Eoc. Eu. 

    †AnguilloididaeAnguilloides M.Eoc.-Mioc. Eu.
        †A. branchiostegalisVeronanguilla 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):