| Scientific Name | Author | English Name |
|---|---|---|
| Ancistroteuthis lichtensteinii | (Férussac, 1835) | Angel squid |
| Callimachus youngorum | Bolstad, 2010 | |
| Filippovia knipovitchi | (Filippova, 1972) | Smooth hooked squid |
| Kondakovia longimana | Filippova, 1972 | Oceanic squid |
| Kondakovia nigmatullini | Laptikhovsky, Arkhipkin & Bolstad, 2009 | |
| Moroteuthopsis ingens | (Smith, 1881) | Greater hooked squid |
| Notonykia africanae | Nesis & Roeleveld/Nikitina, 1998 | |
| Notonykia nesisi | Bolstad, 2007 | |
| Onychoteuthis aequimanus | Gabb, 1868 | |
| Onychoteuthis banksii | (Leach, 1817) | Hooked squid |
| Onychoteuthis bergii | Lichtenstein, 1818 | |
| Onychoteuthis borealijaponica | Okada, 1927 | Boreal clubhook squid |
| Onychoteuthis compacta | (Berry, 1913) | |
| Onychoteuthis lacrima | Bolstad & Seki, 2008 | |
| Onychoteuthis meridiopacifica | Rancurel & Okutani, 1990 | |
| Onychoteuthis mollis | (Appellöf, 1891) | |
| Onychoteuthis prolata | Bolstad, Vecchione & Young, 2008 | |
| Onykia aequatorialis | Thiele, 1921 | |
| Onykia appelloefi | (Pfeffer, 1900) | |
| Onykia carriboea | Lesueur, 1821 | Tropical clubhook squid |
| Onykia indica | Okutani, 1981 | |
| Onykia intermedia | (Pfeffer, 1912) | |
| Onykia loennbergii | (Ishikawa & Wakiya, 1914) | Japanese hooked squid |
| Onykia platyptera | (D'Orbigny, 1834) | |
| Onykia robsoni | (Adam, 1962) | Rugose hooked squid |
| Onykia robusta | (Verrill, 1876) | Robust clubhook squid |
| Onykia verrilli | (Pfeffer, 1900) |