Temporal range: Early Jurassic, 182.7–181.8 Ma
(von Huene, 1931 [originally Stenopterygius h. typicus])
Hauffiopteryx was first described by Michael W. Maisch on the basis of some specimens that previously referred to Stenopterygius hauffianus. Maisch found that the lectotype of S. hauffianus can be determined as Stenopterygius cf. S. quadriscissus at best, and therefore this species should be considered a nomen dubium. He also found out that most specimens previously referred to S. hauffianus can be referred to S. quadriscissus, while the rest belongs to a highly distinctive new taxon that can't be referred to any valid species of Stenopterygius.
Hauffiopteryx is known from the lectotype GPIT 1491/4, articulated complete skeleton which preserved the skull and some soft tissues. The animal is about 1.93 m (6.3 ft) in length. It was collected from the Harpoceras elegantulum-exaratum ammonoid subzones (more specifically Lias ε II4), Harpoceras falcifer zone, of the famous Posidonien-Schiefer lagerstätte (Posidonia Shale) of Holzmaden, dating to the early Toarcian stage of the Early Jurassic, about 182 million years ago. Referred specimens from Holzmaden, Germany and Dudelange, Luxembourg include MHH '9', WAT 1, SMNS 51552, SMNS 80225 and probably the poorly preserved SMNS 81965. They were collected from the Harpoceras semicelatum-elegantulum-exaratum ammonoid subzones (Lias ε II1-5, about 182.7-181.8 mya), Harpoceras tenuicostatum-falcifer zones, of the Posidonia Shale.
Additional materials were described by Hannah Caine and Michael J. Benton in 2011, from the early Toarcian of Strawberry Bank, Ilminster of England. The specimens are all juveniles or infants which preserved almost complete skeletons and some skulls. They include BRLSI M1399 (which was described earlier by Maisch), BRLSI M1400, BRLSI M1401, BRLSI M1403, BRLSI M1404 and BRLSI M1406.
Both the original description by Maisch and the redescription of the English specimens found that Hauffiopteryx might be either a basalmost member of Eurhinosauria or a basalmost member of Thunnosauria (which is an equivalent position to a basalmost member of Stenopterygiidae sensu Maisch  with exclusion of Ichthyosaurus).
Hauffiopteryx was originally recognized by Friedrich von Huene in 1931 as a subspecies of S. hauffianus and named Stenopterygius hauffianus typica. Michael W. Maisch in 2008 elevated it to specific rank and reassigned to its own genus, Hauffiopteryx. The type species is therefore Hauffiopteryx typicus. The generic name honors the Hauff family from Holzmaden, for their generation-long work to increase the knowledge on the Posidonia Shale and its fauna, especially the ichthyosaurs, and pteryx (πτερυξ), Greek for "fin" or "wing". The specific name means typical.
- Michael W. Maisch (2008). "Revision der Gattung Stenopterygius Jaekel, 1904 emend. von Huene, 1922 (Reptilia: Ichthyosauria) aus dem unteren Jura Westeuropas" (PDF). Palaeodiversity. 1: 227–271.
- Hannah Caine and Michael J. Benton (2011). "Ichthyosauria from the Upper Lias of Strawberry Bank, England". Palaeontology. 54 (5): 1069–1093. doi:10.1111/j.1475-4983.2011.01093.x.