- Cunina duplicata Maas, 1893
- Cunina octonaria McCrady, 1859
- Cunina peregrina Bigelow, 1909
- Sigiweddellia bathypelagica Bouillon, Pagès & Gili, 2001 accepted as Sigiweddellia benthopelagica Bouillon, Pagès & Gili, 2001
- Sigiweddellia benthopelagica Bouillon, Pagès & Gili, 2001
- Solmissus incisa (Fewkes, 1886)
- Solmissus incisus (Fewkes, 1886) accepted as Solmissus incisa (Fewkes, 1886)
- Solmissus marshalli Agassiz & Mayer, 1902