Airampoa ayrampo (Azara) Doweld in Turczaninowia 5: 28. 2002 sec. Doweld 2002
- ≡Cactus ayrampo Azara, Voy. Amér. Mér. 2: 526. 1809 syn. sec. Doweld 2002
- ≡Opuntia ayrampo (Azara) Mottram in Tephrocactus Study Group 10: 10. 2004 syn. sec. Doweld 2002
- Neotype (designated by Doweld, A.B. 2002): Peru, Pampa de Arrieros, 23 Aug 1914, J. Rose 18967 (US: 761558)
- =Opuntia haenquiana Herrera in Rev. Univ. Cuzco 8: 60. 1919 syn. sec. Doweld 2002
- =Opuntia soehrensii Britton & Rose, Cactaceae 1: 134-135. 1919 syn. sec. Doweld 2002
- ≡Platyopuntia soehrensii (Britton & Rose) F.Ritter, Kakteen Südamerika 2: 411. 1980 syn. sec. Doweld 2002
- ≡Tunilla soehrensii (Britton & Rose) D.R.Hunt & Iliff in Cactaceae Syst. Init. 9: 11. 2000 syn. sec. Doweld 2002
- ≡Tephrocactus soehrensii (Britton & Rose) G.D.Rowley in Tephrocactus Study Group 12(3): 46. 2006 syn. sec. Kew WCVP (2019)
- ≡Airampoa soehrensii (Britton & Rose) Lodé, Int. Cact. Advent. 111-112: 67. 2016 syn. sec. ???
- =Opuntia poecilacantha Backeb., Cactaceae 6: 6. 1962 syn. sec. Doweld 2002
- =Platyopuntia soehrensii var. grandiflora F.Ritter, Kakteen Südamerika 2: 501. 1980 syn. sec. Kew WCVP (2019)
- =Platyopuntia soehrensii var. transiens F.Ritter, Kakteen Südamerika 3: 888. 1980 syn. sec. Kew WCVP (2019)