In the modern clade Anurognathidae, Anurognathus is the sister taxon of the clade Asiaticognathidae, which contains the species Batrachognathus, Dendrorhynchoides and Jeholopterus.
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Anurognathus was featured in the fifth episode of the ITV science fiction television series Primeval.
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The genus is based on holotype BSP 1922.I.42 (Bayerische Staatssammlung für Palaeontologie und Geologie), found in the Solnhofen limestone near Eichstätt.