A survey of characters defining the Neoteleostei, Eurypterygii, Ctenosquamata, Acanthomorpha, Paracanthopterygii and Acanthopterygii convincingly places the Lampridiformes within the acanthomorph clade. Lampridiforms are primitive with respect to the Percomorpha but their precise placement among basal acanthomorphs remains unclear. In the absence of a specific sister-group hypothesis, Polymixia, percopsiform and beryciform taxa were used as outgroups in a cladistic analysis of the order. Monophyly of Lampridiformes is supported by four apomorphies; three are correlated modifications related to the evolution of a unique feeding mechanism in which the maxilla slides forward with the premaxilla during jaw protrusion. The Veliferidae are the sister group of all other lampridiforms. The deep-bodied (bathysomous) lampridiforms are not monophyletic because Lampris is the sister group of the elongate (taeniosomous) families. Stylephorus is placed as the sister group of all other taeniosomous families. The Radiicephalidae are hypothesized to be the sister group of the Lophotidae, a clade that forms the sister group of the Replecidae + Trachipteridae. Ateleopodid, mirapinnid, and eutaeniiophorid fishes are not lampridiforms. DaggerBajaichthys is allied with living lampridiform fishes but daggerPharmacichthys is not a lampridiform. The affinities of daggerAipichthys and daggerBathysomous are unknown