Morilasi leidub Vaikses, Indias ja Atlandi ookeanis, nad on levinud turskadest ühtlasemalt piki Maailmamerre rannikut ja puuduvad ainult Põhja-Jäämeres ning Antarktika mandrinõlva kohal.
Gadella brocca Paulin & Roberts, 1997.
Gadella dancoheni Sazonov & Shcherbachev, 2000.
Gadella edelmanni (Brauer, 1906).
Gadella filifer (Garman, 1899).
Gadella imberbis (Vaillant, 1888).
Gadella jordani (Böhlke & Mead, 1951).
Gadella macrura Sazonov & Shcherbachev, 2000.
Gadella maraldi (Risso, 1810).
Gadella molokaiensis Paulin, 1989.
Gadella norops Paulin, 1987.
Gadella obscurus (Parin, 1984).
Gadella svetovidovi Trunov, 1992.
Gadella thysthlon Long & McCosker, 1998.
Guttigadus globiceps (Gilchrist, 1906).
Guttigadus globosus (Paulin, 1986).
Guttigadus kongi (Markle & Meléndez C., 1988).
Guttigadus latifrons (Holt & Byrne, 1908).
Guttigadus nudicephalus (Trunov, 1990).
Guttigadus nudirostre (Trunov, 1990).
Guttigadus squamirostre (Trunov, 1990).
Laemonema barbatulum Goode & Bean, 1883.
Laemonema compressicauda (Gilchrist, 1903).
Laemonema filodorsale Okamura, 1982.
Laemonema goodebeanorum Meléndez C. & Markle, 1997.
Laemonema gracillipes Garman, 1899.
Laemonema laureysi Poll, 1953.
Laemonema longipes Schmidt, 1938.
Laemonema macronema Meléndez C. & Markle, 1997.
Laemonema melanurum Goode & Bean, 1896.
Laemonema modestum (Franz, 1910).
Laemonema nana Taki, 1953.
Laemonema rhodochir Gilbert, 1905.
Laemonema robustum Johnson, 1862.
Laemonema verecundum (Jordan & Cramer, 1897).
Laemonema yarrellii (Lowe, 1838).
Laemonema yuvto Parin & Sazonov, 1990.
Lepidion capensis Gilchrist, 1922.
Lepidion ensiferus (Günther, 1887).
Lepidion eques (Günther, 1887).
Lepidion guentheri (Giglioli, 1880).
Lepidion inosimae (Günther, 1887).
Lepidion lepidion (Risso, 1810).
Lepidion microcephalus Cowper, 1956.
Lepidion natalensis Gilchrist, 1922.
Lepidion schmidti Svetovidov, 1936.
Physiculus andriashevi Shcherbachev, 1993.
Physiculus argyropastus Alcock, 1894.
Physiculus beckeri Shcherbachev, 1993.
Physiculus bertelseni Shcherbachev, 1993.
Physiculus capensis (Gilchrist, 1922).
Physiculus chigodarana Paulin, 1989.
Physiculus coheni Paulin, 1989.
Physiculus cyanostrophus Anderson & Tweddle, 2002.
Physiculus cynodon Sazonov, 1987.
Physiculus fedorovi Shcherbachev, 1993.
Physiculus fulvus Bean, 1884.
Physiculus grinnelli Jordan & Jordan, 1922.
Physiculus helenaensis Paulin, 1989.
Physiculus hexacytus Parin, 1984.
Physiculus huloti Poll, 1953.
Physiculus japonicus Hilgendorf, 1879.
Physiculus karrerae Paulin, 1989.
Physiculus kaupi Poey, 1865.
Physiculus longicavis Parin, 1984.
Physiculus longifilis Weber, 1913.
Physiculus luminosus Paulin, 1983.
Physiculus marisrubri Brüss, 1986.
Physiculus maslowskii Trunov, 1991.
Physiculus microbarbata Paulin & Matallanas, 1990.
Physiculus natalensis (Gilchrist, 1922).
Physiculus nematopus Gilbert, 1890.
Physiculus nielseni Shcherbachev, 1993.
Physiculus nigripinnis Okamura, 1982.
Physiculus nigriscens Smith & Radcliffe, 1912.
Physiculus normani Brüss, 1986.
Physiculus parini Paulin, 1991.
Physiculus peregrinus (Günther, 1872).
Physiculus rastrelliger Gilbert, 1890.
Physiculus rhodopinnis Okamura, 1982.
Physiculus roseus Alcock, 1891.
Physiculus sazonovi Paulin, 1991.
Physiculus sterops Paulin, 1989.