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Frailea alacriportana Backeberg & Voll; Arq. Jard. Bot. Rio de Janeiro 9:173-174, tab.8, 1950
= Astrophytum alacriportanum (Backeberg & Voll) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea albiareolata Buining & Brederoo; in Krainz, Die Kakteen. Lief. 53:C VIe, 1973
= Astrophytum albiareolatum (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea albicolumnaris Ritter; Succulenta 49:124, 184-185, 1970
= Astrophytum albicolumnare (F.Ritter) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea albifusca Ritter; Succulenta 49:124, 184-185, 1970
= Astrophytum albifuscum (F.Ritter) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea alexandri Metzing; Bradleya 24: 119-125, 2006

Frailea amerhauseri Prestlé; Succulenta 81: 130-135, 2002

Frailea asperispina Ritter; Succulenta 49:124, 184-185, 1970
= Astrophytum asperispinum (F.Ritter) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea asterioides Werdermann; Feddes Repertorium spec. Nov. 42: 6-7, 1937
= Astrophytum asterioides (Werdermann) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea asterioides var. backebergii Ritter; Kakteen in Sűdamerika 1: 210-211, 1979

Frailea asterioides var. harmoniana Ritter; Kakteen in Sűdamerika 1: 211, 1979

Frailea aurea Backeberg; in Backeberg & Knuth: Kaktus ABC: 247, 415, 1936
= Astrophytum aureum (Backeberg) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea aureinitens Buining & Brederoo; in Succulenta 55(4):62, 1976
= Astrophytum aureinitens (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea aureispina Ritter; Succulenta 49:124, 184-185, 1970
= Astrophytum aureispinum (F.Ritter) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea aureispina var. pallidior Ritter; Succulenta 49:125, 184-185, 1970

Frailea bruchii Spegazzini; Anal. Soc. Cient. Arg. 96: 73-74, 1923
 = Gymnocalycium bruchii (Spegazzini) Hosseus, Revista Centro Estud. Farm. Cordoba 2(6): 22, 1926
= Astrophytum bruchii (Spegazzini) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea buenekeri Abraham; Succulenta 69(3): 64-68, 1980
= Astrophytum buenekeri (Abraham) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea buenekeri ssp. densispina Hofacker & Herm; Kakt. and. Sukk. 48(3): 61-63, 1997

Frailea buiningiana Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 133-135, 1997

Frailea buiningiana f. gracillispina Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 135, 1997

Frailea caespitosa (Spegazzini) Britton & Rose; The Cactaceae 3: 211, 1922
Basionym: Echinocactus caespitosus Spegazzini; Anales Mus. Nac. Buenos Aires 11(Ser. 3a; IV): 495, 1905
= Astrophytum caespitosum (Britton & Rose) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea carminifilamentosa Kilian nom. inval. (Art. 37.1); in Backeberg: Descr. Cact. Nov. 3: 6, 1963
= Astrophytum carminifilamentosum (Kilian in Backeberg) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea carminifilamentosa var. winkelmanniana Kilian nom. inval. (Art. 37.1); in Backeberg: Kakteenlexikon: 159, 1966

Frailea castanea Backeberg; in Backeberg & Knuth: Kaktus ABC: 248, 415, 1936
= Astrophytum castaneum (Backeberg) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea castanea ssp. harmoniana (Ritter) Braun & Esteves; Succulenta 74(3): 130, 1995
Basionym: Frailea asterioides var. harmoniana Ritter

Frailea castanea subvar. spinosior (Ritter) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 214, 1997
Basionym: Frailea perumbilicata var. spinosior Ritter

Frailea castanea var. perumbilicata (Ritter) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 213, 1997
Basionym: Frailea perumbilicata Ritter

Frailea cataphracta (Dams) Britton & Rose; The Cactaceae 3: 210, 1922.
Basionym: Echinocactus cataphractus Dams; Monatsschr. Kakteenkunde 14: 172, 1904
= Astrophytum cataphractum (Dams) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea cataphracta ssp. duchii (Moser) Braun & Esteves; Succulenta 74(3): 130, 1995
Basionym: Frailea cataphracta var. duchii Moser

Frailea cataphracta var. duchii Moser; Nat. Cact. Succ. J. 32(4): 83, 1977

Frailea cataphracta ssp. melitae (Buining & Brederoo) Braun & Esteves; Succulenta 74(3): 130, 1995
Basionym: Frailea melitae Buining & Brederoo

Frailea cataphracta ssp. tuyensis (Buining & Moser) Braun & Esteves; Succulenta 74(3): 130, 1995
Basionym: Frailea cataphracta var. tuyensis Buining & Moser

Frailea cataphracta var. tuyensis Buining & Moser; Succulenta 50(4): 64-65, 50(7): 135, 1971

Frailea cataphractoides Backeberg nom. inval. (Art. 37.1); in Backeberg: Kakteenlexikon: 159, 1966

Frailea chiquitana Cardenás; Nat. Cact. Succ. J. 6(1): 8-9, 1951
= Astrophytum chiquitanum (Cardenás) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea chrysacantha Hrabě nom. inval. (Art. 37.1, 9.5); Kaktusy 1: 131-132, 1965
= Astrophytum chrysacanthum (Hrabě) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea colombiana (Werdermann) Backeberg; in Backeberg & Knuth: Kaktus ABC: 248, 1936
Basionym: Echinocactus colombianus Werdermann; Notizbl. Bot. Gart. U. Mus. Berlin 11: 104, 271-273, 1931

Frailea concepcionensis Buining & Moser; Succulenta 50(3): 49-50, 50(7): 135, 1971

Frailea curvispina Buining & Brederoo; in Krainz, Die Kakteen. Lief. 50-51:C VIe, 1972
= Astrophytum curvispinum (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea deminuta Buining & Brederoo; in Krainz, Die Kakteen. Lief. 54:C VIe, 1973
= Astrophytum deminutum (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea densispina (Hofacker & Herm) Gerloff; Cactus & Co. 3(5): 138-147, 2001
Basionym: Frailea buenekeri ssp. densispina Hofacker & Herm

Frailea friedrichii Buining & Moser; Succulenta 50(2): 25, 50(7): 135, 1971
= Astrophytum friedrichii (Buining & Moser) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea fulviseta Buining & Brederoo; Kakt. and. Sukk. 24: 170-172, 1973
= Astrophytum fulvisetum (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea gracillima (Lemaire) Britton & Rose; The Cactaceae 3: 209, 1922
Basionym: Echinocactus gracillimus Lemaire; Cact. Gen. Nov.: 24, 1839
= Astrophytum gracillimum (Lemaire) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea gracillima ssp. alacriportana (Backeberg & Voll) Gerloff; Mitteilungsblatt Frailea 2(1): 15, 1997
Basionym: Frailea alacriportana Backeberg & Voll

Frailea gracillima ssp. albifusca (Ritter) Braun & Esteves; Succulenta 74(3): 130, 1995
Basionym: Frailea albifusca Ritter

Frailea gracillima ssp. horstii (Ritter) Braun & Esteves; Succulenta 74(3): 130, 1995
Basionym: Frailea horstii Ritter

Frailea gracillima (Monville ex Lemaire) fa. lepida (Buining & Brederoo) Hofacker & Berka, Kaktusy 40(Special 1): 16, 2004
Basionym: Frailea lepida Buining & Brederoo; in Krainz, Die Kakteen. Lief. 54:C VIe, 1973

Frailea grahliana (Haage jr.) Britton & Rose; The Cactaceae 3: 209, 1922
Basionym: Echinocactus grahlianus Haage jr.; Monatsschr. Kakteenkunde 9: 54-57, 1899
= Astrophytum grahlianum (Haage) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea grahliana ssp. concepcionensis (Buining & Moser) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 190, 1997
Basionym:Frailea concepcionensis Buining & Moser

Frailea grahliana ssp. moseriana (Buining & Brederoo) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 196, 1997
Basionym: Frailea moseriana Buining & Brederoo

Frailea grahliana var. rubrispina (Schelle) Y. Ito; Expl. Diagr. 233, 1957

Frailea grahliana ssp. ybatense (Buining & Moser) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 195, 1997
Basionym: Frailea ybatense Buining & Moser

Frailea hlineckyana Červinka;Frailea 1971(2): 13, 1971

Frailea horstii Ritter; Succulenta 49:124, 184-185, 1970
= Astrophytum horstii (Ritter) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea horstii ssp. fecotrigensis Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 131-132, 1997

Frailea ignacionensis Buining & Moser; Succulenta 50(4): 63-64, 50(7): 135, 1971
= Astrophytum ignacionensis (Buining & Moser) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea jajoiana Červinka;Frailea 1971(2): 13-14, 1971

Frailea knippeliana (Quehl) Britton & Rose; The Cactaceae 3: 211, 1922
Basionym: Echinocactus knippelianus Quehl; Monatsschr. Kakteenkunde 12: 9, 1902
= Astrophytum knippelianum (Quehl) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea larae Vasquez; Revist. Soc. Estud. Bot. 1: 5-8, 1994

Frailea lepida Buining & Brederoo; in Krainz, Die Kakteen. Lief. 54:C VIe, 1973
= Astrophytum lepidum (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea mammifera Buining & Brederoo; in Krainz, Die Kakteen. Lief. 50-51:C VIe, 1972
= Astrophytum mammiferum (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea mammifera subsp. angelesiae R.Kiesling & Metzing; Cact. Syst. Init. 21:17-18, 2006
= Frailea angelesii R. Kiesling ex Prestlé; nom. inval (Arts 36.1, 37.1)

Frailea matoana Buining & Brederoo; Cact. Succ. J. (US) 43: 139-142, 1971
= Astrophytum matoanum (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea melitae Buining & Brederoo; Kakt. and. Sukk. 25(6): 121-123, 1974
= Astrophytum melitae (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea moseriana Buining & Brederoo; in Krainz, Die Kakteen. Lief. 50-51:C VIe, 1973
= Astrophytum moseranum (Buining & Brederoo) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea odieri (Lemaire ex Saml-Dyck) Spegazzini; Anal. Soc. Cient. Arg. 99: 131, 1925
Basionym: Echinocactus odieri Lemaire ex Saml-Dyck; Cact. Hort. Dyck. 1849
= Eriosyce odieri (Lemaire ex Saml-Dyck) Kattermann; Succulent Plant Research 1: 158, 1994

Frailea perbella Prestlé; Succulenta 59 (5): 115-120, 1980
= Astrophytum perbellum (Prestlé) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea perumbilicata Ritter; Succulenta 49:125, 184-185, 1970
= Astrophytum perumbilicatum (Ritter) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea perumbilicata var. spinosior Ritter; Succulenta 49:125, 184-185, 1970

Frailea phaeodisca (Spegazzini) Spegazzini; Anal. Soc. Cient. Arg.96: 72-73, 1923
Basionym: Echinocactus pygmaeus var. phaeodiscus Spegazzini; Anales Mus. Nac. Buenos Aires 3(4): 498, 1905
Frailea phaeodisca (Spegazzini) Y. Ito nom. illeg.; Expl. Diagr. 237, 1957
= Astrophytum phaeodiscum (Spegazzini) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea pseudogracillima Ritter; Kakteen in Sűdamerika 1: 201, 1979
= Astrophytum pseudogracillimum (Ritter) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea pseudopulcherrima Frič ex Y. Ito; Expl. Diagr. 294, 1957
= Astrophytum pseudopulcherrimum (Ritter) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea pulcherrima (Arechavaleta) Spegazzini; Anal. Soc. Cient. Arg.99: 131, 1925
Basionym: Echinocactus pulcherrimus Arechavaleta; Anales Mus. Nac. Montevideo, 222-226, 1905
= Malacocarpus pulcherrimus (Arechavaleta) Britton & Rose; The Cactaceae 3: 194, 1922
= Astrophytum pulcherrimum (Arechavaleta) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea pullispina Backeberg nom. inval. (Art. 8.2); in Backeberg: Descr. Cact. Nov. 3: 6, 1963
= Astrophytum pullispinum (Backeberg) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea pullispina var. atrispina Backeberg nom. inval. (Art. 43.1); in Backeberg: Descr. Cact. Nov. 3: 6, 1963

Frailea pullispina var. centrispina Backeberg nom. inval. (Art. 43.1); in Backeberg: Descr. Cact. Nov. 3: 6, 1963

Frailea pumila (Lemaire) Britton & Rose; The Cactaceae 3: 209, 1922
Basionym: Echinocactus pumilus Lemaire; Cact. Aliq. Nov.: 21, 1838
= Astrophytum pumilum (Lemaire) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea pumila ssp. albiareolata (Buining & Brederoo) Braun & Esteves; Succulenta 74(3): 130, 1995
Basionym: Frailea albiareolata Buining & Brederoo

Frailea pumila ssp. colombiana (Werdermann) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 156, 1997
Basionym: Echinocactus colombianus Werdermann

Frailea pumila ssp. deminuta (Buining & Brederoo) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 170, 1997
Basionym: Frailea deminuta Buining & Brederoo

Frailea pumila var. gracillima (Lemaire) Y. Ito; Expl. Diagr. 233, 1957
Basionym: Echinocactus pumilus var. gracillima (sic!) (Lemaire) Schumann; Gesamtbeschreibung: 394, 1898

Frailea pumila ssp. hlineckyana (Červinka) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 159, 1997
Basionym: Frailea hlineckyana Červinka

Frailea pumila ssp. jajoiana (Červinka) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 160, 1997
Basionym: Frailea jajoiana Červinka

Frailea pumila ssp. maior (Ritter) Braun & Esteves; Succulenta 74(3): 130-131, 1995
Basionym: Frailea pumila var. maior Ritter

Frailea pumila var. maior Ritter; Kakteen in Sűdamerika 1: 206, 1979

Frailea pygmaea (Spegazzini) Britton & Rose; The Cactaceae 3: 210-211, 1922
Basionym: Echinocactus pygmaeus Spegazzini; Anales Mus. Nac. Buenos Aires 3(4): 497-498, 1905
= Astrophytum pygmaeum (Spegazzini) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea pygmaea ssp. albicolumnaris (Ritter) Hofacker; Cact. Cons. Init. 6(12): 11, 1998
Basionym: Frailea albicolumnaris Ritter

Frailea pygmaea ssp. altigibbera (Ritter) Braun & Esteves; Succulenta 74(3): 131, 1995
Basionym: Frailea pygmaea v. altigibbera Ritter

Frailea pygmaea ssp. asperispina (Ritter) Braun & Esteves; Succulenta 74(3): 131, 1995
Basionym: Frailea asperispina Ritter

Frailea pygmaea var. atrofusca Backeberg; Die Cactaceae 3: 1660, 1959
Basionym: Frailea pygmaea var. atrofusca Backeberg nom. inval.; in Backeberg & Knuth: Kaktus ABC: 250, 1936

Frailea pygmaea var. aurea (Backeberg) Backeberg ; Die Cactaceae 3: 1661, 1959
Basionym: Frailea aurea Backeberg

Frailea pygmaea ssp. aureinitens (Buining & Brederoo) Braun & Esteves; Succulenta 74(3): 131, 1995
Basionym: Frailea aureinitens Buining & Brederoo

Frailea pygmaea ssp. aureispina (Ritter) Braun & Esteves; Succulenta 74(3): 131, 1995
Basionym: Frailea aureispina Ritter

Frailea pygmaea var. curvispina Ritter; Kakteen in Sűdamerika 1: 204, 1979

Frailea pygmaea var. dadakii (Frič ex Berger) Backeberg ; Die Cactaceae 3: 1660, 1959
Basionym: Echinocactus dadakii Frič ex Berger nom. inval. (Art. 34); in Berger: Kakteen: 218, 341, 1929
= Astrophytum dadakii (Frič) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea pygmaea ssp. fulviseta (Buining & Brederoo) Braun & Esteves; Succulenta 74(3): 131, 1995
Basionym: Frailea fulviseta Buining & Brederoo

Frailea pygmaea ssp. lilalunula (Ritter) Braun & Esteves; Succulenta 74(3): 131, 1995
Basionym: Frailea pygmaea  var. lilalunula Ritter

Frailea pygmaea var. lilalunula Ritter; Kakteen in Sűdamerika 1: 203, 1979

Frailea pygmaea var. longispina Ritter; Kakteen in Sűdamerika 1: 204, 1979

Frailea pygmaea var. maior Ritter; Kakteen in Sűdamerika 1: 204, 1979

Frailea pygmaea var. phaeodisca (Spegazzini) Y. Ito Cacti: 70. 1952
Basionym: Echinocactus pygmaeus var. phaeodiscus Spegazzini; Anales Mus. Nac. Buenos Aires 3(4): 498, 1905

Frailea pygmaea var. planicostata Ritter; Kakteen in Sűdamerika 1: 204, 1979

Frailea pygmaea var. pulcherrima (Arechavaleta) Prestlé; in Prestlé, Die Gattung Frailea, ed. 2, 84, 1997
Basionym: Echinocactus pulcherrimus Arechavaleta

Frailea pygmaea ssp. tuyensis (Buining & Moser) Metzing; Cact. Syst. Init. 21:16, 2006
Basionym: Frailea cataphracta v. tuyensis Buining & Moser
= Frailea cataphracta ssp. tuyensis (Buining & Moser) P.J. Braun & Esteves

Frailea schilinzkyana (Haage jr.) Britton & Rose; The Cactaceae 3: 210, 1922
Basionym: Echinocactus schilinzkyanus Haage jr.; Monatsschr. Kakteenkunde 7: 108, 1897
= Cactus schilinzkyanus (Haage jr.) Kuntze; Deutsch. Bot. Monatsschrift 21: 172-173, 1903
= Astrophytum schilinzkyanum (Haage) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea schilinzkyana ssp. concepcionensis (Buining & Moser) Braun & Esteves; Succulenta 74(3): 131, 1995
Basionym:Frailea concepcionensis Buining & Moser

Frailea schilinzkyana (Haage jr.) Britton & Rose ssp.matoana (Buining & Brederoo) Berka, Kaktusy 40(Special 1): 14, 2004
Basionym: Frailea matoana Buining & Brederoo; Cact. Succ. J. (US) 43: 139-142, 1971

Frailea schilinzkyana var. grandiflora (Haage jr.) Y. Ito; Expl. Diagr. 233, 1957

Frailea uhligiana Backeberg nom. inval. (Art. 8.2); in Backeberg: Descr. Cact. Nov. 3: 6, 1963
= Astrophytum uhligianum (Backeberg) J.J.Halda et M.Malina; Acta Mus. Richnov., sect. Natur 12(1):11-15, 2005

Frailea ybatense Buining & Moser; Succulenta 50(3): 46-47, 50(7): 135, 1971