= Andinopuntia floccosa (Salm-Dyck) Guiggi; Cactology 2(Suppl.): (1) (2011)
= Andinopuntia floccosa subsp. yanganucensis (Rauh & Backeb.) Guiggi; Cactology 5(Suppl. II): 1 (2016)
= Austrocylindropuntia floccosa subsp. crispicrinitus (Rauh & Backeb.) Ostolaza; Cactus Perú 156 (2014)
= Austrocylindropuntia floccosa subsp. yanganucensis (Rauh & Backeb.) Ostolaza; Cactaceae Syst. Init. 24: 6 (2008)
= Austrocylindropuntia hirschii (Backeb.) E.F.Anderson; Cact. Succ. J. (Los Angeles) 71(6): 324 (1999)
= Austrocylindropuntia lagopus f. rauhii (Backeb.) F.Ritter; Kakteen Südamerika 4: 1243 (1981) (without basionym vol. or page:)
= Austrocylindropuntia machacana F.Ritter; Kakteen Südamerika 4: 1246 (1981)
= Austrocylindropuntia punta-caillan (Rauh & Backeb.) E.F.Anderson; Cact. Succ. J. (Los Angeles) 71(6): 324 (1999)
= Austrocylindropuntia tephrocactoides Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 6 (1957)
= Austrocylindropuntia yanganucensis (Rauh & Backeb.) E.F.Anderson; Cact. Succ. J. (Los Angeles) 71(6): 324 (1999)
= Cylindropuntia tephrocactoides (Rauh & Backeb.) Rauh & Backeb.; Sitzungsber. Heidelberger Akad. Wiss., Math.-Naturwiss. Kl., Abh. 1 (Beitr. Peruan. Kakt.): 194 (1958)
= Maihueniopsis floccosus (Salm-Dyck) Kiesling; (1998)
= Opuntia atroviridis f. longicylindrica (Rauh & Backeb.) Krainz; Kakteen [H.Krainz] 44-45: ? (1970)
= Opuntia atroviridis f. parviflora (Rauh & Backeb.) Krainz; Kakteen [H.Krainz] 44-45: ? (1970)
= Opuntia atroviridis f. paucispina (Rauh & Backeb.) Krainz; Kakteen [H.Krainz] 44-45: ? (1970)
= Opuntia atroviridis Werderm. & Backeb.; Neue Kakteen 63 (1931), et Repert. Spec. Nov. Regni Veg. 30: 59 (1932)
= Opuntia blancii (Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia crispicrinita (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia crispicrinita subvar. flavicoma (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia crispicrinita var. cylindracea (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia crispicrinita var. tortispina (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia cylindrolanata (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia floccosa Salm-Dyck; Allg. Gartenzeitung [Otto & Dietrich] 13: 888 (1845)
= Opuntia floccosa subvar. aurescens (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia floccosa var. canispina (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia floccosa var. cardenasii (Marn.-Lap.) G.D.Rowley; Repert. Pl. Succ. 22: 11 (1973), basionym without type.
= Opuntia floccosa var. crassior (Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia floccosa var. denudata F.A.C.Weber; Dict. Hort. [Bois] 2: 897 (1898)
= Opuntia floccosa var. ovoides (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia hempeliana K.Schum.; Gesamtbeschr. Kakt. 690 (1898)
= Opuntia hirschii (Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 5 (1958)
= Opuntia lagopus var. aureopenicillata (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 6 (1958)
= Opuntia pseudoudonis (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 6 (1958)
= Opuntia punta-caillan (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 6 (1958)
= Opuntia rauhii (Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 6 (1958)
= Opuntia tephrocactoides (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 4 (1958)
= Opuntia udonis Weing.; Kakteenkunde 71 (1933)
= Opuntia verticosa Weing.; Kakteenkunde 72 (1933)
= Opuntia yanganucensis (Rauh & Backeb.) G.D.Rowley; Natl. Cact. Succ. J. 13: 6 (1958)
= Tephrocactus atroviridis (Werderm. & Backeb.) Backeb.; Kaktus-ABC [Backeberg & Knuth] 105 (1935)
= Tephrocactus atroviridis var. longicylindricus Rauh & Backeb.; Sitzungsber. Heidelberger Akad. Wiss., Math.-Naturwiss. Kl. 1958(1): 212 (1958)
= Tephrocactus atroviridis var. parviflorus Rauh & Backeb.; Sitzungsber. Heidelberger Akad. Wiss., Math.-Naturwiss. Kl. 1958(1): 213 (1958)
= Tephrocactus atroviridis var. paucispina Rauh & Backeb.; Sitzungsber. Heidelberger Akad. Wiss., Math.-Naturwiss. Kl. 1958(1): 214 (1958)
= Tephrocactus blancii Backeb.; Descr. Cact. Nov. [Backeberg] 1: 8 (1956 publ. 1957)
= Tephrocactus crispicrinitus Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 7 (1957)
= Tephrocactus crispicrinitus subvar. flavicomus Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 7 (1956 publ. 1957)
= Tephrocactus crispicrinitus var. cylindraceus Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 7 (1956 publ. 1957)
= Tephrocactus crispicrinitus var. tortispinus Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 7 (1956 publ. 1957)
= Tephrocactus cylindrolanatus Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 7 (1956 publ. 1957)
= Tephrocactus floccosus (Salm-Dyck) Backeb.; Möller´s Deutsche Gärtn.-Zeitung 49: 105 (1934), nomen, et Kaktus-ABC [Backeberg & Knuth] 105 (1935)
= Tephrocactus floccosus subvar. aurescens Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 7 (1956 publ. 1957)
= Tephrocactus floccosus var. canispinus Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 6 (1956 publ. 1957)
= Tephrocactus floccosus var. crassior Backeb.; Cactus (Paris) 38: 249 (1953)
= Tephrocactus floccosus var. denudatus (F.A.C.Weber) Backeb.; Cactaceae [Backeberg] 1: 235 (1958)
= Tephrocactus floccosus var. ovoides Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 7 (1956 publ. 1957)
= Tephrocactus hirschii Backeb.; Descr. Cact. Nov. [Backeberg] 8 (1957)
= Tephrocactus lagopus var. aureopenicillatus Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 7 (1956 publ. 1957)
= Tephrocactus pseudoudonis Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 7 (1957)
= Tephrocactus punta-caillan Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 8 (1957)
= Tephrocactus rauhii Backeb.; Cact. Succ. J. Gr. Brit. 18: 122 (1956)
= Tephrocactus udonis (Weing.) Backeb.; Kaktus-ABC [Backeberg & Knuth] 106 (1935)
= Tephrocactus verticosus (Weing.) Backeb.; Kaktus-ABC [Backeberg & Knuth] 106 (1935)
= Tephrocactus yanganucensis Rauh & Backeb.; Descr. Cact. Nov. [Backeberg] 1: 8 (1956 publ. 1957)