Nomenclature:

Hennediella Paris, Index Bryol.: 557. 1896. Hennedia R. Br. bis, Trans. & Proc. New Zealand Inst. 25: 285. 1893, nom. illeg. (non Hennedya Harv., Trans. Roy. Irish Acad. 22 (Sci.): 552. 1855).?LECTOTYPE, designated by Zander, 1993: Hennediella macrophylla (R. Br. bis) Paris.
Beckettia Müll. Hal., Hedwigia 37: 77. 1898. Hennediella subgen. Beckettia (Müll. Hal.) G. Roth, Die Aussereur. Laubm.: 219. 1911.?TYPE: Beckettia bruchioides Müll. Hal.
Neobarbula Dusén, Bot. Not. 1905: 299. 1905. Tortula sect. Neobarbula (Dusén) Cardot, Wiss. Erg. Schwed. Südpolar-Exp. 4(8): 95. 1908.?TYPE: Neobarbula magellanica Dusén.
Willia sect. Schistidiella Müll. Hal., Gen. Musc. Frond.: 424. 1901(1900). Willia subgen. Schistidiella (Müll. Hal.) Broth. in Engl. & Prantl (eds.), Nat. Pflanzenfam. 1(3): 417. 1902.?TYPE: Willia marginata (Hook. f. & Wilson) Müll. Hal.