Eumandya parva (Sasaki, 1914)
Eumandya phenax (G. L. Voss, 1962)
Euprymna albatrossae G. L. Voss, 1962
Euprymna berryi Sasaki, 1929
Euprymna hoylei Adam, 1986
Euprymna morsei (A. E. Verrill, 1881)
Euprymna parva (Sasaki, 1913) accepted as Eumandya parva (Sasaki, 1914)
Euprymna penares (Gray, 1849)
Euprymna phenax G. L. Voss, 1962 accepted as Eumandya phenax (G. L. Voss, 1962)
Euprymna pusilla (Pfeffer, 1884) (uncertain > nomen dubium )
Euprymna schneehagenii (Pfeffer, 1884) (uncertain > nomen dubium )
Euprymna scolopes S. S. Berry, 1913
Euprymna stenodactyla (R. E. Grant, 1833)
Euprymna tasmanica (Pfeffer, 1884)
Inioteuthis capensis G. L. Voss, 1962 accepted as Rondeletiola capensis (G. L. Voss, 1962)
Inioteuthis japonica (Tilesius, 1845)
Inioteuthis maculosa E. S. Goodrich, 1896
Lusepiola birostrata (Sasaki, 1918)
Lusepiola trirostrata (G. L. Voss, 1962)