In synonymy:
Anchognatha Thorell, 1881 = Nyssus Walckenaer, 1805 (Raven, 2015: 129)
Supunna Simon, 1897 = Nyssus Walckenaer, 1805 (Raven, 2015: 129)

type Nyssus coloripes Walckenaer, 1805; gender masculine

N.B.: considered a senior synonym of Anchognatha Thorell, 1881: 228 [urn:lsid:nmbe.ch:spidergen:02517] (type A. avida Thorell, 1881 ) and of Supunna Simon, 1897a: 168 [urn:lsid:nmbe.ch:spidergen:02269] (type Agroeca insularis L. Koch, 1873, listed by Brignoli in Micariinae (Gnaphosidae)) by Raven, 2015: 129; see discussion about priority over Supunna in Raven, 2015: 21.

In synonymy:
Nyssus albomaculatus (Rainbow, 1902, T from Supunna) = Nyssus albopunctatus (Hogg, 1896) (Raven, 2015: 142).
Nyssus auripes (Rainbow, 1916, T from Storena) = Nyssus coloripes Walckenaer, 1805 (Raven, 2015: 132).
Nyssus bicolor (Hogg, 1900, T from Medmassa) = Nyssus coloripes Walckenaer, 1805 (Raven, 2015: 132).
Nyssus funereus (Simon, 1896, T from Supunna) = Nyssus albopunctatus (Hogg, 1896) (Raven, 2015: 142).
Nyssus michaelseni (Simon, 1909, T from Supunna) = Nyssus coloripes Walckenaer, 1805 (Raven, 2015: 132).
Nyssus pictus (L. Koch, 1873, T from Supunna) = Nyssus coloripes Walckenaer, 1805 (Raven, 2015: 131).
Nyssus variepes (Rainbow, 1912, T from Storena) = Nyssus coloripes Walckenaer, 1805 (Davies, 1985: 119, sub Supunna picta).
Nyssus versicolor (Simon, 1896, T from Supunna) = Nyssus coloripes Walckenaer, 1805 (Raven, 2015: 132).

Liocranum albopunctatum Hogg, 1896: 328 (Df).
Supunna funerea Simon, 1896b: 407 (Df; N.B.: described in generic nomen nudum) [urn:lsid:nmbe.ch:spidersp:025474].
Supunna albopunctata Simon, 1897a: 168.
Supunna funerea Simon, 1897a: 160, f. 160.
Storena albomaculata Rainbow, 1902c: 485, pl. 18, f. 1 (Df) [urn:lsid:nmbe.ch:spidersp:025471].
Supunna albomaculata Davies, 1985: 119 (Tf from Storena).
Nyssus albopunctatus Raven, 2015: 142, f. 79b, 80a-e, 135 (f, Dm, S).

Anchognatha avida Thorell, 1881: 229 (Df).
Nyssus avidus Raven, 2015: 148, f. 79d, 82a-d (f, Dm).

Nyssus coloripes Walckenaer, 1805: 52 (Df; N.B.: considered a nomen dubium by Roewer, 1955c: 1605).
Agelena coloripes Walckenaer, 1841: 25.
Agroeca picta L. Koch, 1873: 438, pl. 34, f. 5 (Df) [urn:lsid:nmbe.ch:spidersp:025477].
Supunna versicolor Simon, 1896b: 407 (Df; N.B.: described in generic nomen nudum) [urn:lsid:nmbe.ch:spidersp:025479].
Supunna coloripes Simon, 1897a: 168.
Supunna picta Simon, 1897a: 168.
Medmassa bicolor Hogg, 1900: 112, pl. 16, f. 4 (Df) [urn:lsid:nmbe.ch:spidersp:025285].
Supunna michaelseni Simon, 1909d: 175 (Df) [urn:lsid:nmbe.ch:spidersp:025476].
Storena variepes Rainbow, 1912a: 192, f. 1-2 (Df).
Storena auripes Rainbow, 1916a: 45, pl. 14, f. 16-18 (Dm) [urn:lsid:nmbe.ch:spidersp:041306].
Supunna picta Forster, 1979: 94, f. 24, 152, 357-361 (f, Dm).
Supunna picta Davies, 1985: 119 (S).
Supunna picta Paquin, Vink & Dupérré, 2010: 70, f. 42.1-4 (mf).
Nyssus coloripes Raven, 2015: 131, f. 2a, 4f, 5c, 6c,, 7f, 73a-d, 74a-g, 135 (f, Sm).

Nyssus emu Raven, 2015: 164, f. 91a-b (Dm).

Agroeca insularis L. Koch, 1873: 437 (Dj).
Supunna insularis Simon, 1897a: 168.
Nyssus insularis Raven, 2015: 150, f. 16b, 83a-d, 87e-f (Df).

Nyssus jaredwardeni Raven, 2015: 137, f. 16c, 75a-e, 76a-b (Dmf).

Nyssus jonraveni Raven, 2015: 146, f. 81f-h (Dm).

Nyssus loureedi Raven, 2015: 155, f. 86a-e, 87a-d (Dmf).

Nyssus luteofinis Raven, 2015: 138, f. 77a-e, 79a (Dmf).

Nyssus paradoxus Raven, 2015: 158, f. 88a-e, 89a-c, 135 (Dmf).

Nyssus pseudomaculatus Raven, 2015: 144, f. 81a-e (Dmf).

Nyssus robertsi Raven, 2015: 159, f. 89d-e (Df).

Nyssus semifuscus Raven, 2015: 140, f. 78a-d (Dmf).

Nyssus wendyae Raven, 2015: 162, f. 90a-b (Dm).

Nyssus yuggera Raven, 2015: 152, f. 1c, 5f, 7a-c, 84a-e, 85a-d, 135 (Dmf).