= Chilita alamensis (R.T.Craig) Buxb.; Sukkulentenkunde 5: 16 (1954)
= Chilita gueldemanniana (Backeb.) Buxb.; Sukkulentenkunde 5: 15 (1954)
= Chilita inaiae (R.T.Craig) Buxb.; Sukkulentenkunde 5: 15 (1954)
= Chilita sheldonii (Britton & Rose) Orcutt; Cactography 2 (1926)
= Chilita swinglei (Britton & Rose) Orcutt; Cactography 2 (1926)
= Cochemiea swinglei (Britton & Rose) Doweld; Sukkulenty (Moscow) 3: 39 (2000)
= Ebnerella guirocobensis (R.T.Craig) Buxb.; Oesterr. Bot. Z. 98: 89 (1951)
= Ebnerella inaiae (R.T.Craig) Buxb.; Oesterr. Bot. Z. 98: 89 (1951)
= Ebnerella sheldonii (Britton & Rose) Buxb.; Oesterr. Bot. Z. 98: 90 (1951)
= Ebnerella swinglei (Britton & Rose) Buxb.; Oesterr. Bot. Z. 98: 90 (1951)
= Mammillaria alamensis R.T.Craig; Mammill. Handb. 299 (1945)
= Mammillaria dioica subsp. swinglei (Britton & Rose) Hoeve; J. Mammillaria Soc. 53(1): 16 (2013)
= Mammillaria grahamii subsp. sheldonii (Britton & Rose) D.R.Hunt; Cactaceae Syst. Init. 20: 21 (2005)
= Mammillaria gueldemanniana Backeb.; Beitr. Sukkulentenk. Sukkulentenpflege 57 (1941)
= Mammillaria gueldemanniana var. guirocobensis (R.T.Craig) Backeb.; Cactaceae [Backeberg] 5: 3336 (1961)
= Mammillaria guirocobensis R.T.Craig; Mammill. Handb. 220 (1945)
= Mammillaria inaiae R.T.Craig; Cact. Succ. J. (Los Angeles) 10: 111 (1939)
= Mammillaria marnieriana Backeb.; Cactus (Paris) 31(Suppl.): 2 (1952)
= Mammillaria microcarpa f. gueldemanniana (Backeb.) Neutel.; Succulenta (Netherlands) 65(1): 4 (1986)
= Mammillaria microcarpa f. swinglei (Britton & Rose) Neutel.; Succulenta (Netherlands) 65: 4 (1986), no basionym ref.
= Mammillaria microcarpa var. sheldonii (Britton & Rose) Neutel.; Succulenta (Netherlands) 65: 3 (1986), no basionym ref.
= Mammillaria milleri f. gueldemanniana (Backeb.) Neutel.; Succulenta (Netherlands) 65: 119 (1986)
= Mammillaria milleri f. swinglei (Britton & Rose) Neutel.; Succulenta (Netherlands) 65: 119 (1986)
= Mammillaria milleri var. sheldonii (Britton & Rose) Neutel.; Succulenta (Netherlands) 65: 119 (1986)
= Mammillaria sheldonii (Britton & Rose) Boed.; Mammillarien-Vergleichs-Schlüssel 30 (1933), Issue 145
= Mammillaria swinglei (Britton & Rose) Boed.; Mammillarien-Vergleichs-Schlüssel 33 (1933), Issue 145
= Mammillaria swinglei var. diabloa P.C.Fisch.; Cact. Succ. J. (Los Angeles) 64(5): 246, 245 (1992)
= Neomammillaria alamensis (R.T.Craig) Y.Itô; Cactaceae [Itô] 597 (1981), without basionym ref.
= Neomammillaria inaiae (R.T.Craig) Y.Itô; Cactaceae [Itô] 606 (1981), without basionym ref.
= Neomammillaria sheldonii Britton & Rose; Cactaceae [Britton & Rose] 4: 156 (1923)
= Neomammillaria swinglei Britton & Rose; Cactaceae [Britton & Rose] 4: 158 (1923)