The concept for a family of "double canined" early therocephalians was first put forward by Broom in 1908, when he proposed that the "double canined" early therocephalians recognised at the time (
Lycosuchus,
Hyaenasuchus and
Trochosuchus) formed a separate evolutionary unit from other early therocephalians, then recognised as the "
Pristerognathidae" (now known as Scylacosauridae). Broom would continue to be a proponent for this division, but for many decades he did not attribute a name to such a group, even after Lycosuchidae was already made available. The family Lycosuchidae was first established by Baron
Franz Nopcsa in 1923, although the name was often misattributed to other authors by later researchers until the end of the 20th century when his precedent was recognised. Other early uses of the name Lycosuchidae were by
Samuel W. Williston in his 1925 publication
The Osteology of the Reptiles, and a similar concept was used by
Sidney H. Haughton and Adrian S. Brink in 1954 catalogue of fossil "reptiles" from the Karoo, though neither of them attributed any authorship to Lycosuchidae. Therein, he also established the taxonomically higher group
Lycosuchia (originally "Lycosauria" in his thesis) containing the family, intended to be the equivalent
sister group to
Scylacosauria, though this higher taxon has not seen use since then. Two genera are considered valid today,
Lycosuchus and
Simorhinella, each with a single species (
monospecific). Both genera were named by
Robert Broom, a
palaeontologist who worked on and named many Karoo fossils, in the early 20th century (1903 and 1915, respectively), but
Simorhinella was not actually identified as a lycosuchid until almost a century after its discovery.
Lycosuchus is known from five skulls and mandibles of varying completeness, including the nearly complete
holotype. An alternative but functionally identical name for the family,
Trochosuchidae, was established by
Alfred Romer in 1956, apparently unaware of the pre-existing use of Lycosuchidae by other authors. Romer named the family after
Trochosuchus, a now
dubious genus of lycosuchid. Curiously, Romer would erect a family for the lycosuchid genera for a second time in 1966, this time as
Trochosauridae after the lycosuchid
Trochosaurus (also now dubious). Romer likely did this because in 1966 he felt that
Trochosuchus was distinct from other lycosuchids and instead assigned it to another family, the
Alopecodontidae (a family otherwise made up of what are now scylacosaurids). This is despite the fact that Romer had previously considered the genera
Trochosuchus and
Trochosaurus synonymous while under Trochosuchidae. Although Lycosuchidae has
priority over either name, some authors perpetuated the use of Trochosuchidae and Trochosauridae, including some who used the former well after Romer proposed replacing it with Trochosauridae (e.g.
Charles Lewis Camp and colleagues in 1968 and 1972). The dubiousness of all other historically named lycosuchids is in part due to the often poor quality of their
type material, which are often incomplete and badly weathered. Another confounding factor is that several were primarily or entirely distinguished based only on features such as the relative proportions of the canines, snout, and number of postcanine teeth—features now known to be individually variable, subject to
taphonomic distortion, and associated tooth replacement—as is the case for
Trochosuchus,
Trochosaurus and
Trochorhinus. Not all specimens of
Scymnosaurus represent lycosuchids, however, and a third dubious species,
S. watsoni, is based on the fossils of an indeterminate scylacosaurid. Nonetheless, a revision of Scylacosauridae in 2023 by Christian F. Kammerer has explicitly defined Scylacosauridae to exclude
Lycosuchus as a distinct phylogenetic unit. However, this result was only recovered under the majority rule consensus (i.e. it was not recovered in every iteration of the analysis), and it has only been recovered once since then. Indeed, most subsequent analyses of this dataset (such as Liu and Abdala, 2023, below right cladogram) have found
Gorynychus to be placed intermediately between
Lycosuchus and Scylacosauria (as would be the suggested position of
Simorhinella).
Gorynychus was also assigned to Lycosuchidae by Julia Suchkova and Valeriy Golubev in 2018, independently of these phylogenetic results, when they named
G. sundyrensis. However, this was based entirely on anatomical similarities and was not supported by any phylogenetic analysis. of the possible lycosuchid
Gorynychus with hypothetical fur, note the "double canines" in
G. sundyrensis, inferred from its fossils }} ==Evolution and extinction==