After Grimaldi & Engel, 2005 (based on Zwick, 2000)

<==o Plecoptera Latreille, 1902 sensu lato [incl.? †“Protoperlaria]  (koskikorennot; stoneflies)
   |--o †Lemmatophoridae Sellards 1909 [Ortaidae Sellards, 1909; Lecoriidae Handlirsch, 1919] [paraphyletic †“Protoperlaria”]
   |  |--o †Lemmatophora Sellards 1909
   |  |  `-- †T. typa Sellards 1909 [T. typica Tillyard 1928; T. anomala; T. elongata; T. delicosa; T. hirsuta, Sellards, 1909]
   |  |--o †Artinska Sellards 1909 [Estadia Sellards, 1909; Lectrum Sellards, 1909; Orta Sellards, 1909]
   |  |  `-- †A. clara Sellards 1909 [A. medialis Sellards, 1909; A. gracilis Sellards, 1909; A. pecta Sellards, 1909; A. major Sellards, 1909; A. extensa Sellards, 1909; Estadia elongata Sellards, 1909;, E. arcuata Sellards, 1909; E. tenuis Sellards, 1909; Estadia tripunctata Carpenter 1926; Lectrum anomalum Sellards, 1909]
   |  `--o †Lisca Sellards, 1909
   |     `-- †L. minuta Sellards, 1909 [Lemmatophora reducta Tillyard 1928; L. minuta Tillyard 1928; L. cubitalis Handlirsch 1937]
   |--o †Liomopteridae Sellards, 1909 [paraphyletic †“Protoperlaria”]
   |  `--o †Liomopterum Sellards 1909 [Horates Sellards, 1909]
   |     `-- †L. ornatum Sellards, 1909 [L. extensum Sellards, 1909]
   `--+--o †Probnidae Sellards, 1909 [nom. correct. pro Probnisidae Sellards 1909]
      |  `--o †Probnis Sellards 1909 [= Espira Sellards 1909; Stoichus Sellards 1909; Stinus Sellards 1909]
      |     `-- †P. speciosa Tillyard 1937 [P. coriacea Sellards, 1909; Espira obscura Sellards, 1909; Stoichus elegans Sellards, 1909; S. arcuatus Sellards, 1909; S. minor Sellards, 1909; S. tenuis Sellards, 1909; Stinus brevi-cubitalis Sellards 1909; Probnis sellardsi Handlirsch 1919]
      `--o Plecoptera sensu Grimaldi & Engel, 2005
         |-- †Palaeonemouridae
         |-- †Palaeoperlidae
         |-- †Perlopseidae
         `--+--o Antarctoperlaria sensu lato
            |  |-- †“Eusthenioides”
            |  |-- †Euxenoperlidae
            |  `--+?- †Siberioperlidae Sinitshenkova, 1983
            |     `--o Antarctoperlaria
            |        |--o Eusthenioidea
            |        |  |-- Eustheniidae
            |        |  `-- Diamphipnoidae
            |        `--o Leptoperloidea [Griphopterygoidea]
            |           |-- Austroperlidae
            |           `-- Gripopterygidae
            `--o Arctoperlaria
               |--o Systellognatha [Subulipalpia]?
               |  |?- †Platyperlidae
               |  `--+--+-- Pteronarcyidae
               |     |  `--+-- Peltoperlidae
               |     |     `--o Styloperlidae
               |     |        |-- Styloperla
               |     |        `-- Cerconychia 
               |     `--+-- Perlodidae
               |        |-- Perlidae
               |        `-- Chloroperlidae
               `--o Euholognatha
                  |-- Scopuridae
                  `--o Nemouroidea?
                     |?- †Perlariopseidae
                     |-- Taeniopterygidae
                     `--+?- †Baleyopterygidae
                        |--+-- “Notonemouridae”
                        |  `-- Nemouridae
                        `--+-- Capniidae
                           `-- Leuctridae

Alternative phylogeny after Parker, 1982, and Nelson, 1996-1998 [“The Tree of Life”]

<==o Plecoptera [incl.? †“Protoperlaria”]  (koskikorennot; stoneflies) 
   |--o Eusthenioidea
   |  |-- Eustheniidae
   |  `-- Diamphipnoidae
   `--+--o Leptoperloidea
      |  |-- Austroperlidae
      |  `-- Gripopterygidae
      `--o EUHOLOGNATHA? [paraphyletic?]
         |-- Scopuridae
         |--o NEMOUROIDEA?
         |  |-- Taeniopterygidae
         |  `--+--+-- Notonemouridae
         |     |  `-- Nemouridae
         |     `--+-- Capniidae
         |        `-- Leuctridae
         `--o SYSTELLOGNATHA [Subulipalpia]?
            |-- Pteronarcyidae
            `--+--+-- Peltoperlidae
               |  `--o Styloperlidae
               |     |-- Styloperla
               |     `-- Cerconychia 
               `--+-- Perlodidae
                  |-- Perlidae
                  `-- Chloroperlidae

Reference(s):