Referred specimens from Holzmaden, Germany and Dudelange, Luxembourg include MHH '9', WAT 1, SMNS 51552, SMNS 80225 and probably the poorly preserved SMNS 81965.
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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 2008 with exclusion of Ichthyosaurus).