Class Conjugatophyceae Engl. (1892)
see Class Zygnematophyceae Round ex Guiry (2013)
01 Order Zygnematales - filamentous conjugates and saccoderm desmids
02 Order Desmidiales - placoderm desmids
03 Genus Astrocosmium Stockmayer (1888), incertae sedis
04 Genus †Baccinellula Weyland (1963), incertae sedis
05 Genus †Closterimopsis L.M. Yin & Z.P. Li (1978), incertae sedis
06 Genus †Desmidopsis L.M. Yin & Z.P. Li (1978), incertae sedis
07 Genus Didymidium P.F. Reinsch (1867), incertae sedis
08 Genus †Paleospiralis incertae sedis
09 Genus Phycastrum Kützing ex Kützing (1849), incertae sedis
10 Genus Phycoleda Itzigs. (1854), incertae sedis
11 Genus Polysolenia C.G. Ehrenberg ex F.T. Kützing (1849), incertae sedis
12 Genus Schizospora P.F. Reinsch, 1874-1875, incertae sedis
13 Genus †Spirogyrites Shukla (1950), incertae sedis
14 Genus Spirotaenia Bréb. ex Ralfs (1848), incertae sedis
15 Genus †Stenixys T.M.Harris (1938), incertae sedis