Maisch and Matzke (2000) and Maisch (2010) regarded "Chacaicosaurus" and "Hauffiopteryx" to be stenopterygiids. However, they didn't perform any cladistic analyses to confirm these claims. Fischer "et al." (2011) performed a cladistic analysis that found "Chacaicosaurus" to be a basal thunnosaur which is placed outside both Stenopterygiidae and Ophthalmosauridae. Both Maisch (2008) and Caine and Benton (2011) performed cladistic analyses that found "Hauffiopteryx" to 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"). These results mean that the Stenopterygiidae are a monotypic family that includes only the type genus "Stenopterygius".