After Palker, 1982, Grimaldi & Engel, 2005, and Engel & Grimaldi, 2007

<==o Neuroptera Linnaeus sensu stricto? [Planipennia] (verkkosiipiset (harsosiipiset); lacewings, antlions, owflies, etc.)
   |?- †Mesohemerobius jeholensis Ping, 1928; L.Cret. EAs. [Neuroptera incertae sedis (Makarkin et al., 2003)]
   |-- †“Permithonidae”
   `--+--o Nevrorthidae Nakahara [Neurorthidae (lapsus calami)] [Nevorthiformia]
      |  |-- †Rophalis relicta (Hagen); M.Eoc. NEu.
      |  |-- Austroneurorthus
      |  |--o Nevorthus
      |  |  `-- N. fallax
      |  `-- Nipponeurorthus
      `--+?- †Grammosmylidae
         |--o Hemerobiiformia (harsokorentomaiset)
         |  |?- †“Osmylitidae”
         |  `--+?-o †Prohemerobiidae
         |     |  `-- †Prohemerobius Handlirsch, 1906
         |     |?- †“Archaeosmyluscomplesus Whalley, 1988
         |     |?- †“Archaeosmylusalysius Whalley, 1988
         |     |--+--o Ithonoidea
         |     |  |  |-- Polystoechotidae Handlirch 1906 (giant lacewings)
         |     |  |  `-- Ithonidae Newman, 1853 [incl. Rapismatidae Krüger, 1922] (moth lacewings)
         |     |  `--+-- Chrysopidae Schneider (green lacewings; harsokorennot)
         |     |     `--o Osmyloidea
         |     |        |==o †Archeosmylidae Riek, 1953 [probably paraphyletic basal Osmyloids]
         |     |        |  |--o †Archaeosmylus Riek, 1953; L.Perm.-E.Jur. Aust.
         |     |        |  |  |-- †A. pectinatus Reik, 1953
         |     |        |  |  |?- †A. stigmatus Reik, 1955
         |     |        |  |  |?- †A. costalis Reik, 1955
         |     |        |  |  `?- †A. sp. (L.Trias. Aust)
         |     |        |  |?- †Archeosmylidae gen. et sp. indet. (L.Perm. South Africa)
         |     |        |  |-- †Babykamenia eskovi Ponomarenko & Shcherbakov, 2004
         |     |        |  `?-o †Lithosmylidia Reik, 1955; M.-L.Trias. Aust.
         |     |        |     |-- †L. lineata Reik, 1955
         |     |        |     |?- †L. barrone Lambkin, 1988
         |     |        |     `?- †L. parvula Lambkin, 1988
         |     |        `--o Osmylidae Leach, 1815 (osmylids)
         |     |           |-- †Archaeosmylidia fusca Makarkin, Yang & Ren, 2012; M.Jur. EAs.
         |     |           `--+?- †Tetanoptilon Bode, 1953
         |     |              |-- †Osmalochrysa Jepson, Makarkin & Coram, 2012
         |     |              |?-o †Mesosmylininae
         |     |              |  |-- †Mesosmylina Bode, 1953
         |     |              |  |-- †Sogjuta Martynova, 1958
         |     |              |  `-- †Petrushevskia Martynova, 1958
         |     |              |?-o †Saucrosmylinae Ren & Yin, 2003
         |     |              |  |-- †Saucrosmylus sambneurus Ren & Yin, 2003; M.Jur. EAs.
         |     |              |  |-- †Rudiosmylus ningchengensis Ren & Yin, 2003; M.Jur. EAs.
         |     |              |  |-- †Laccosmylus calophlebius Ren & Yin, 2003; M.Jur. EAs.
         |     |              |  `--o †Bellinympha Y. Wang, Ren, Liu, Shih & Engel, 2010 in Y. Wang, Liu, X. Wang, Shih, Zhao, Engel & Ren, 2010; M.Jur. EAs.
         |     |              |     |-- †B. filicifolia Y. Wang, Ren, Liu, Shih & Engel, 2010 in Y. Wang, Liu, X. Wang, Shih, Zhao, Engel & Ren, 2010
         |     |              |     `-- †B. dancei Y. Wang, Ren, Liu, Shih & Engel, 2010 in Y. Wang, Liu, X. Wang, Shih, Zhao, Engel & Ren, 2010
         |     |              |--o Protosmylinae
         |     |              |  |-- Gryposmylus
         |     |              |  |-- Heterosmylus
         |     |              |  |-- Paryphosmylus
         |     |              |  |-- †Juraheterosmylus
         |     |              |  |-- †Mesosmylus
         |     |              |  |-- †Osmylidia
         |     |              |  |-- †Protosmylina
         |     |              |  `--o †Protosmylus
         |     |              |     `-- †P. pictus (Hagen); M.Eoc. NEu.
         |     |              |--o Gumillinae
         |     |              |--o Spilosmylinae
         |     |              |  `-- Thyridosmylus
         |     |              |-- Kempyninae
         |     |              |-- Porismus strigatus (Burmeister, 1839) [Porisminae]
         |     |              |-- Stenosmylinae
         |     |              |-- Eidoporisminae
         |     |              `--o Osmylinae
         |     |                 `--o Osmylus
         |     |                    `-- O. fulvicephalus
         |     `--+-- Hemerobiidae Latreille [Hemerobioidea] (brown lacewings; kirvakorennot)
         |        `--+--+--o Sisyridae (spongillaflies; rantakorennot)
         |           |  |  |?- †Cratosisyrops L.Cret. ESA. (incertae sedis)
         |           |  |  |?- †Sisyra? amissa Hagen; M.Eoc. NEu.
         |           |  |  |== numerous Eocene fossil genera
         |           |  |  |?- Climacia
         |           |  |  |?- Sisyra
         |           |  |  `== numerous Recent genera
         |           |  `-- Coniopterygidae Burmeister [Coniopterygoidea] (dustywings; vahakorennot)
         |           `--o Mantispoidea
         |              |--o Dilaridae Newman (pleasing lacewings)
         |              |  |--o Nallachiinae
         |              |  |  `--o Nallachius
         |              |  |     `-- N. americanus
         |              |  `--o Dilarinae
         |              |     |-- †Cascadilar eocenicus Engel, 1999; M.Eoc. NEu.
         |              |     `--o Dilar
         |              |        `-- D. septentrionalis
         |              `--+-- Mantispidae Leach (mantispids; rukoilijakorennot)
         |                 `--+-- †“Mesithonidae”
         |                    `--+--o Rhachiberothidae Tjeder (thorny lacewings)
         |                       |  |-- †Paraberotha acra Whalley; L.Cret. SWAs.
         |                       |  |-- †Retinoberotha stuermeri Schlüter; U.Cret. WEu.
         |                       |  |-- †Eorhachiberotha burmitica Engel, 2004; U.Cret. SEAs.
         |                       |  |-- †Rhachibermissa splendida Grimaldi; U.Cret. ENAm.
         |                       |  |-- †Whalfera venatrix (Whalley; 1983) M.Eoc. NEu.
         |                       |  |-- †Alloberotha petrulevicii Nel et al., 2005; U.Cret. WEu.
         |                       |  |-- †Chimerhachiberotha acrasarii Nel et al., 2005; L.Cret. SWAs.
         |                       |  |-- †Spinoberotha mickaelacrai Nel et al., 2005; L.Cret. SWAs.
         |                       |  |-- †Oisea celinea (Nel et al., 2005) Eoc. WEu.
         |                       |  `== Recent genera
         |                       `--o Berothidae Handlirsch (beaded lacewings)
         |                          |?- †Banoberotha enigmatica Whalley; U.Cret. SWAs..
         |                          |?-o †Jersiberotha Grimaldi; U.Cret. NAm.
         |                          |  |-- †J. luzzii Grimaldi
         |                          |  `-- †J. similis Grimaldi
         |                          |?- †Nascimberotha picta Grimaldi; U.Cret. NAm.
         |                          |?- †Microberotha macculloughi Archibald & Makarkin; Eoc.
         |                          |?- †Plesiorobius? anadensis Klimaszewski & Kevan; U.Cret. NAm.
         |                          |?- †Proberotha prisca Krüger, 1923; M.Eoc. NEu.
         |                          |?- Lomamyia
         |                          |-- Cyrenoberothinae
         |                          |-- Berothinae
         |                          |-- Nosybinae
         |                          |-- Nyrminae
         |                          |-- Protobiellinae
         |                          `-- Trichomatinae
         `--o Myrmeleontiformia (muurahaiskorentomaiset)
            |?- †Aetheogramma speciosa Ren & Engel, 2008 [Aetheogrammatidae Ren & Engel, 2008]
            `--o Myrmeleontoidea
               |--o Nemopteroidea
               |  |--o †Kalligrammatidae Handlirsch, 1906
               |  |  |--o †Kalligrammatinae Handlirsch, 1906
               |  |  |  |-- †Huiyingogramma formosum Liu et al., 2014
               |  |  |  |--o †Kalligramma Walther, 1904
               |  |  |  |  `-- †K. paradoxum Liu et al., 2014
               |  |  |  |--o †Limnogramma Ren, 2003
               |  |  |  |  |-- †L. hani
               |  |  |  |  |-– †L. mira
               |  |  |  |  `-- &38224;L. mongolicum
               |  |  |  |--o †Meioneurites Handlirsch, 1906; L.Jur. CAs.
               |  |  |  |  |-- †M. (Parameioneurites) spectabilis Engel, 2005
               |  |  |  |  |-- †M. schlosseri Handlirsch, 1906
               |  |  |  |  `-- †M. villosus Panfilov, 1980
               |  |  |  |-- †Protokalligramma bifasciatum Yang, Makarkin & Ren, 2011
               |  |  |  `--o †Sophogramma Ren & Guo, 1996
               |  |  |     |-- †S. papilionaceum Ren & Guo, 1996
               |  |  |     `-- †S. wimbledoni Jepson, Makarkin & Coram, 2012
               |  |  `--o †Kallihemerobiinae Ren & Engel, 2008
               |  |     |-- †Apochrysogramma rotundum Yang, Makarkin & Ren, 2011
               |  |     `-– †Kallihemerobius pleioneurus Ren & Oswald, 2002
               |  `--+-- Psychopsidae Handlirsch (silky lacewings)
               |     `-- Nemopteridae (spoon-, thread-winged lacewings; lippukorennot)
               `--+--o †Osmylopsychopidae
                  |  `-- †Petropsychops superba Trias. Aust.
                  |-- †Nymphitidae
                  |-- †“Solenoptilidae”
                  |-- †Brogniartiellidae
                  `--+--o Nymphidae Rambur [incl. Myiodactylidae] (split-footed lacewings)
                     |  |-- †Pronymphes mengeanus (Hagen); M.Eoc. NEu.
                     |  |-- Nymphes
                     |  |-- Myiodactylus
                     |  |-- Osmylops
                     |  `== numerous other Recent genera
                     `--+-- †Babinskaiidae
                        |--o Myrmeleontidae Latreille [incl. †Palaeoleontidae] (antlions; muurahaiskorennot, -leijonat)
                        |  |?- †Samsonileon fragmentus Ponomarenko; L.Cret. SWAs. [Palaeoleontidae]
                        |  |?- †Palaeoleon ferrogeneticus Rice; U.Cret. NENAm. [Palaeoleontidae]
                        |  |?- †Dendroleon septemmontanus Statz, 1936
                        |  |?-o Porrelus
                        |  |  |-- †P. dominicanus Poinar & Stange, 1996; Mioc. CAm.
                        |  |  `== recent Porrelus -species
                        |  |?- Dimarinae
                        |  |?- Stilbopteryginae
                        |  |?- Pseudimarinae
                        |  |?- Echthromyrmicinae
                        |  |?- Palparinae [incl. †Araripeneurinae]
                        |  |?- Myrmecaelurinae
                        |  |?- Acanthaclisinae
                        |  |?- Myrmeleontinae
                        |  |?- Brachynemurinae
                        |  |?- Dendroleontinae
                        |  |?- Glenurinae
                        |  `?- Nemoleontinae
                        `--o Ascalaphidae Rambur (owlflies; pöllökorennot)
                           |?- †Ascaloptynx oligocenicus Nel, 1990; Olig. WEu.
                           |?- †Borgia proavus (Hagen, 1858) Navás, 1913; Olig. CEu.
                           |?- †Mesascalaphus yangi Ren et al., 1995; U.Jur. EAs.
                           |?- †Neadelphus protae MacLeod, 1970; M.Eoc. NEu. [larva]
                           |?- †Prosuhpalacsa biamoensis Makarkin, 1998; ?U.Olig.-?L.Mioc. EAs.
                           |?- †Ricartus edwardsi (Oustalet, 1870) Navás, 1913; Olig. WEu.
                           |?- Cordulecerus
                           |?- Albardiinae
                           |--o Ascalaphinae
                           |  |--o Ululodes
                           |  |  `-- †U. paleonesia Engel & Grimaldi, 2007; Mioc. CAm.
                           |  `== Other Ascalaphines
                           `--o Haplogleniinae
                              |--o Amoea
                              |  `-- †A. electrodominicana Engel & Grimaldi, 2007; Mioc. CAm.
                              `== Other Haplogleniines

Reference(s):