The study of Plourdosteus canadensis (Brachythoraci, Placodermi) from the Escuminac Formation (Frasnian) led us to erect a new family: the Plourdosteidae. Firstly, we discuss all the characteristics that allowed Ørvig to differentiate the genus Plourdosteus from Coccosteus. It is proposed to consider Plourdosteus mironovi as a synonym of Plourdosteus trautscholdi, found in the Baltic region of the USSR. The characteristics that support the monophyly of the Plourdosteidae are listed and are represented on a phylogenetic diagram. In the conclusion, the Dunkleosteidea sup. fam. nov., the Plourdosteidae fam. nov., and the type species Plourdosteus canadensis are defined. The different species of Plourdosteus are also listed.