Synechodus was named by Woodward (1888) [Sepkoski's age data: K Apti T Dani Sepkoski's reference number: 884]. It is not extant.

It was assigned to Cestraciontidae by Woodward (1889), Chapman (1918) and Leriche (1942); to Notidanidae by Casier (1958); to Heterodontidae by Jordan (1963); to Synechodontidae by Herman (1977) and Case (1978); to Palaeoniscidae by Delsate and Godefroit (1995); to Galeomorphii by Sepkoski (2002); to Synechodontiformes by Duffin (1998), Underwood et al. (1999) and Delsate (2003); to Paleospinacidae by Underwood (2002) and Ginter et al. (2010); and to Palaeospinacidae by Cappetta (1975), Müller and Diedrich (1991), Duffin and Ward (1993), Johns (1997), Underwood and Mitchell (1999), Rees (2000), Peng et al. (2001), Delsate et al. (2002), Kriwet (2003), Underwood (2004), Yamagishi (2004), Underwood and Ward (2004), Rees (2005), Ivanov (2005), Klug (2008), Guinot et al. (2013), Guinot et al. (2014), Siversson et al. (2015), Siversson and Machalski (2017), Cappetta et al. (2019), Hoganson et al. (2019) and Ebersole et al. (2022).