Specimens of Hexostoma thynni (Delaroche, 1811) Rafinesque, 1815 were collected from their type-host, the bluefin tuna Thunnus thynnus, caught off Algeria, i.e. close to the type-locality, off Mallorca, which is also in the Mediterranean. The species is briefly redescribed and compared to previous descriptions, under the same name or as its synonym Plagiopeltis duplicata Diesing, 1858, to ascertain identity of specimens. The three genera within the Hexostomatidae (Hexostoma Rafinesque, 1815, Neohexostoma Price, 1961 and Homostoma Unnithan, 1965) are briefly discussed, with comments on the fragility of characters used to distinguish them. Using next-generation sequencing, the complete mitogenome and the cluster of ribosomal genes (SSU, LSU, ITS1, ITS2, 5.8S) were obtained. The mitogenome is 14,649 bp long and codes for 12 protein-coding genes, 2 ribosomal RNA genes and 22 transfer RNA genes; its size is similar to other mitogenomes obtained from polyopisthocotylean monogeneans. A phylogeny based on concatenated mitogenome protein-coding genes from nine species of polyopisthocotylean monogeneans produced a tree in which the Hexostomatidae H. thynni was associated with other Mazocraeidea, such as Chauhaneidae and Diclidophoridae. This invalidates the hypothesis of Boeger & Kritsky (1993) of Hexostomatidae as sister-group to the Mazocraeidea and suggests the demise of the suborder Hexostomatinea Boeger & Kritsky, 1993. We insist on the usefulness of depositing parts of specimens used for molecular analyses, prepared on permanent slides, in a curated collection.