[1] The skeleton was discovered during the early 19th Century,[3] in beds of the famous Posidonien-Schiefer lagerstätte at Holzmaden, Baden-Württemberg, in southeastern Germany.

It is known from the holotype and only specimen, MMUM LL 8004, an almost complete, three-dimensionally preservedand and articulated skeleton, found from the Hildoceras bifrons Zone (181.2–180.7 Ma) of the Alum Shale Member, Whitby Mudstone Formation, dating to early Toarcian stage.

The holotype and only specimen of H. longirostris, MCZ 1033, found from the Harpoceras serpentinum Zone (182.7–181.2 Ma) of the Jet Rock Member, Whitby Mudstone Formation, early Toarcian of Yorkshire, England.

[6] Few Early Jurassic plesiosaurians have the sort of long, thin snout present in Hauffiosaurus, a shape usually considered to indicate a diet of fish (ichthyophagy).

Cladogram after Benson et al., 2011:[2] Anningasaura Attenborosaurus Plesiosauroidea Atychodracon Archaeonectrus Macroplata "Plesiosaurus" macrocephalus H. longirostris H. tomistomimus H. zanoni Maresaurus Meyerasaurus Rhomaleosaurus Eurycleidus Pliosauridae With the description of Marmornectes in 2011, Ketchum & Benson suggested for the first time that many basal plesiosaurs and pliosauroids are members of Pliosauridae and Rhomaleosauridae.

[8] Anningasaura "Plesiosaurus" macrocephalus Archaeonectrus Macroplata Atychodracon Eurycleidus Rhomaleosaurus Meyerasaurus Maresaurus Thalassiodracon H. longirostris H. tomistomimus H. zanoni Attenborosaurus advanced pliosaurids