Grusonia, Cactaceae 1: 215. 1919 sec. Hunt (2006)
- Type: Grusonia bradtiana
- =Corynopuntia, Kaktus ABC: 114, 410. 1936 syn. sec. Hunt (2006)
- Type: Corynopuntia clavata
- =Micropuntia in Amer. Midl. Naturalist 36: 661. 1946 syn. sec. Hunt (2006)
- =Marenopuntia in Desert Pl. Life 22: 27. 1950 syn. sec. Hunt (2006)
- Type: Marenopuntia marenae
Corynopuntia was included in Grusonia s.l. (Wallace & Dickie 2002; Anderson 2001, 2005; Nyffeler & Eggli 2010), then accepted as separate genus by Hunt (2006). Griffith & Porter (2009) argue for recognizing Corynopuntia as a distinct genus, and Grusonia as monotypic, although support for the monophyly of Corynopuntia was only 67% BS in their study. Their data also suggest that Micropuntia could be recognised as a separate genus. Bárcenas & al. (2011) do not find support for treating Corynopuntia separate from Grusonia, and in addition find no support for a monophyletic Corynopuntia, therefore the circumscription of Corynopuntia needs to be clarified still.