Order Squatiniformes Compagno, 1973
Order Squatiniformes Compagno, 1973, J.Linn.Soc.(Zool.), 53, suppl. 1.
Synonymy:
Order Asterospondyli, Suborder Rhinae: Gill, 1893
Order Cyclospondyli, Suborder Tectospondyli: Jordan and Evermann, 1896
Order Euselachii, Suborder Squatinoidei: Blot, 1969
Order Lamniformes, Suborder Squatinoidei: Patterson, 1967
Suborder Plagiostomi Tectospondyli: Hasse, 1879 (in part)
Suborder Rajiformes: Goodrich, 1909 (in part)
Suborder Rhinae: Gill, 1862, 1872
Suborder Rhiniformes: Lozano y Rey, 1928
"Group" Rhinoidei: Garman, 1913
Order Squalea, Suborder Rhinida: White, 1936, 1937
Order Squaliformes, Suborder Squatinoidei: Berg, 1940, Berg and Svedovidov, 1955, Arambourg and Bertin, 1958 (in part)
Order Squaloidea, Suborder Squatinoidea: Schultz and Stern, 1948
Suborder Squaloidea: Romer, 1945, 1966 (in part), Norman, 1966 (in part)
"Division" Squaloidei: Regan, 1906 (in part)
Suborder Squaloidei: Engelhardt, 1913 (in part)
Order Squatinae: Fowler, 1941, Smith, 1949
Order Squatinida, Suborder Squatinoidei: Glikman, 1967
Order Squatiniformes: Rass and Lindberg, 1971, Applegate, 1974, Chu and Wen, 1979
Suborder Squatiniformes: Bertin, 1939
Suborder Squatinina: Matsubara, 1955, Fowler, 1969a
Suborder Squatinoidea: Bigelow and Schroeder, 1948
Suborder Squatinoidei: Lindberg, 1971, Nelson, 1976
Order Tectospondyli, Suborder Squatinoidei: Jordan, 1923.