Original description as Cyprinus viviparus:
- Bustamante, M.. 1837. "Descripción del Mexcalpique (Cyprinus viviparus)". Mosaico Mexicano. 2:116 (ffm04515)
- Girardinichthys innominatus Bleeker, 1860, with type locality at Mexico City, Mexico. Determiner: Álvarez del Villar et al., 1957
- Limnurgus variegatus Günther, 1866, with type locality at Vicinity of Mexico City, Mexico. Determiner: Álvarez del Villar et al., 1957
- Characodon geddesi Regan, 1904, with type locality at Lake Tezcoco [should be Texcoco], southern Mexico. Determiner: Álvarez del Villar et al., 1957
- Girardinichthys limnurgus Jordan & Everman, 1927, with type locality at Lake Lerma, Mexico. Determiner: Radda et al., 2003
Conservation: Girardinichthys viviparus is evaluated by the international union for the conservation of nature in the iucn red list of threatened species as (CR) critically endangered (1996). The habitats in the Parque de Chapultepec are under pressure by exotic species, polluted water, water treatment and parasites. Nevertheless, the population in the Lago Mayor seems to be stable and quite good in stock. Scientists document big populations and good stocks at Alameda Oriente and in the Lake of Tecocomulco, whereas in the lakes Xochimilco and Zumpango the populations are very small and under pressure of exotic species, industrial waste water (especially with heavy metals) and eutrophication. Other existing populations are not reported, some are said to be extinct already by the named factors.