After Nelson, 1994, and Javonillo, Malabarba, Weitzman & Burns, 2010, with Recent species from Froese & Pauly, 2001 [“The FishBase”]

<==o Gasteropelecidae (hatchetfishes; tapparatetrat/-kalat)
   |--o Triportheini Géry, 1977
   |  |?- Lignobrycon myersi (Miranda-Ribeiro, 1956)
   |  `--o Triportheus Mioc. Pleist. R. SA.
   |     |-- †T. ligniticus
   |     |-- T. albus Cope, 1872
   |     |-- T. angulatus (Spix & Agassiz, 1829)
   |     |-- T. culter (Cope, 1872)
   |     |-- T. curtus (Garman, 1890)
   |     |-- T. elongatus (Günther, 1864) (Elongate hatchetfish)
   |     |-- T. guentheri (Garman, 1890)
   |     |-- T. magdalenae (Steindachner, 1878)
   |     |-- T. nematurus (Kner, 1858)
   |     |-- T. paranensis (Günther, 1874)
   |     |-- T. pictus (Garman, 1890)
   |     |-- T. rotundatus (Jardine, 1841)
   |     |-- T. signatus (Garman, 1890)
   |     `-- T. trifurcatus (Castelnau, 1855)
   `--+-- Gnathocharax steindachneri Fowler, 1913
      `--o Gasteropelecidae sensu stricto?
         |--o Carnegiella
         |  |-- G. marthae Myers, 1927 (kääpiötapparakala; Blackwing hatchetfish)
         |  |-- G. myersi Fernández-Yépez, 1950 Pygmy hatchetfish
         |  |-- G. schereri Fernández-Yépez, 1950 Dwarf hatchetfish
         |  `-- G. strigata (Günther, 1864) (marmoritapparatetra; Marbled hatchetfish)
         `--+--o Thoracocharax
            |  |-- T. securis De Filippi, 1853 (isotapparatetra; Giant hatchetfish)
            |  `-- T. stellatus (Kner, 1858) (Spotfin hatchetfish; tähtitapparakala)
            `--o Gasteropelecus
               |-- G. levis (Eigenmann, 1909) (hopeatapparatetra; Silver hatchetfish)
               |-- G. maculatus Steindachner, 1879 Spotted hatchetfish
               `-- G. sternicla (Linnaeus, 1758) (tapparakala; River hatchetfish)

Note:

Fishbase don't include genus Triportheus in the family Gasteropelecidae, all other sources I got do.

Reference(s):