= Calacinum complexum (A.Cunn.) J.F.Macbr.; Publ. Field Mus. Nat. Hist., Bot. Ser. 4: 115 (1927)
= Fallopia ×complexa (A.Cunn.) J.-M.Tison; Evaxiana 8: 224 (2021)
= Muehlenbeckia complexa var. grandifolia Carse; Trans. New Zealand Inst. 47: 239 (1915)
= Muehlenbeckia complexa var. microphylla (Colenso) Cockayne; Trans. New Zealand Inst. 48: 208 (1916)
= Muehlenbeckia complexa var. trilobata (Colenso) Cheeseman; Man. New Zealand Fl., ed. 2: 402 (1925)
= Muehlenbeckia debilis Petrie; Trans. & Proc. New Zealand Inst. 56: 10 (1926)
= Muehlenbeckia ephedroides var. muricatula (Colenso) Cheeseman; Man. New Zealand Fl. 594 (1906)
= Muehlenbeckia microphylla Colenso; Trans. & Proc. New Zealand Inst. 20: 204 (1887 publ. 1888)
= Muehlenbeckia paucifolia Colenso; Trans. & Proc. New Zealand Inst. 21: 99 (1888 publ. 1889)
= Muehlenbeckia trilobata Colenso; Trans. & Proc. New Zealand Inst. 21: 100 (1888 publ. 1889)
= Muehlenbeckia truncata Colenso; Trans. & Proc. New Zealand Inst. 21: 101 (1888 publ. 1889)
= Muehlenbeckia varians Meisn.; Bot. Zeitung (Berlin) 10: 347 (1852)
= Muehlenbeckia ×austracompla Allan; Genetica 8: 531 (1926)
= Muehlenbeckia ×muricatula Cockayne & Allan; Trans. & Proc. New Zealand Inst. 57: 71 (1927), nom. illeg.
= Muehlenbeckia ×muricatula Colenso; Trans. & Proc. New Zealand Inst. 22: 482 (1889 publ. 1890)
= Polygonum camptianum Meisn.; Prodr. [A.P. de Candolle] 14: 147 (1857)
= Polygonum complexum A.Cunn.; Ann. Nat. Hist., Sér. 1: 1: 455 (1838)
= Polygonum comptonianum Meisn.; Prodr. [A.P. de Candolle] 14: 147 (1856), nom. inval.
= Polygonum cordatum Meisn.; Prodr. [A.P. de Candolle] 14: 146 (1856), nom. inval.
= Polygonum heterophyllum Sol. ex Meisn.; Prodr. [A.P. de Candolle] 14: 147 (1857)
= Polygonum rotundifolium Bosse; Vollst. Handb. Bl.-gärtn., ed. 3, 3: 179 (1861)
= Polygonum varians (Meisn.) Kuntze; Revis. Gen. Pl. 2: 559 (1891)
= Sarcogonum complexum (A.Cunn.) Kunze; Linnaea 17: 570 (1843)