1. Family Asyncorynidae Kramp, 1949
2. Family Ceratelladae Gray, 1868 accepted as Solanderiidae Marshall, 1892 (synonym)
3. Family Cladocorynidae Allman, 1872
4. Family Cladonematidae Gegenbaur, 1857
5. Family Cladonemidae accepted as Cladonematidae Gegenbaur, 1857 (incorrect spelling variant)
6. Family Cladosarsiidae Bouillon, 1978 accepted as Corynidae Johnston, 1836
7. Family Codonidae Haeckel, 1879 accepted as Corynidae Johnston, 1836 (synonym)
8. Family Corynidae Johnston, 1836
9. Infraorder Corynipteridae accepted as Zancleidae Russell, 1953 (invalid name)
10. Family Dendronemidae Haeckel, 1879 accepted as Cladonematidae Gegenbaur, 1857 (synonym)
11. Family Discalidae Haeckel, 1888 accepted as Porpitidae Goldfuss, 1818 (synonym)
12. Family Eleutheriidae Russell, 1953 accepted as Cladonematidae Gegenbaur, 1857 (synonym)
13. Family Halimedusidae Arai & Brinckmann-Voss, 1980
14. Family Halocordylidae Stechow, 1921 accepted as Pennariidae McCrady, 1859 (synonym)
15. Family Halocorynidae Picard, 1957 accepted as Zancleidae Russell, 1953 (synonym)
16. Family Hydrocorynidae Rees, 1957
17. Family Milleporadae Fleming, 1828 accepted as Milleporidae Fleming, 1828 (incorrect formation of family name)
18. Family Milleporidae Fleming, 1828
19. Superfamily Moerisiida Poche, 1914 (invalid grouping (polyphyletic))
20. Family Moerisiidae Poche, 1914
21. Infraorder Orthocorynidae accepted as Zancleidae Russell, 1953 (invalid name)
22. Family Pennariidae McCrady, 1859
23. Family Polyorchidae Agassiz, 1862 accepted as Corynidae Johnston, 1836 (synonym)
24. Family Porpalidae Haeckel, 1888 accepted as Porpitidae Goldfuss, 1818 (synonym)
25. Infraorder Porpitae accepted as Porpitidae Goldfuss, 1818 (incorrect family name formation, emended to Porpitidae by Guilding (1828))
26. Family Porpitellidae Haeckel, 1888 accepted as Porpitidae Goldfuss, 1818 (synonym)
27. Family Porpitidae Goldfuss, 1818
28. Family Pseudosolanderiidae Bouillon & Gravier-Bonnet, 1988
29. Family Pteronemidae Haeckel, 1979
30. Family Rosalindidae Bouillon, 1985
31. Family Sarsiadae Forbes, 1848 accepted as Corynidae Johnston, 1836 (synonym)
32. Family Solanderiidae Marshall, 1892
33. Superfamily Sphaerocorynida Petersen, 1990 (unfounded grouping)
34. Family Sphaerocorynidae Prévot, 1959
35. Family Syncorynidae Allman, 1872 accepted as Corynidae Johnston, 1836 (synonym)
36. Family Teissieridae Bouillon, 1978
37. Family Tricyclusidae Kramp, 1949
38. Family Velellidae Eschscholtz, 1829 accepted as Porpitidae Goldfuss, 1818 (synonym)
39. Superfamily Zancleida Russell, 1953 (unfounded grouping)
40. Family Zancleidae Russell, 1953
41. Family Zancleopsidae Bouillon, 1978

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