The most complete Ordovician vertebrate known to date is Sacabambaspis janvieri. This jawless fish, like heterostracans, possesses dorsal and ventral shields made up of large median plates. Anteriorly, the dorsal shield delimits an elliptical space that contains the eyeballs with their dermal sclerotic and scleral ossifications, and the paired olfactory capsules. The anterior part of the ventral shield is composed of square-shaped platelets aligned in rows to form an exoskeletal mouth apparatus resembling that of heterostracans. S. janvieri may have a lateral series of 20 branchial plates and its bone is cellular. All the Ordovician vertebrates were previously classified with the heterostracans. Our present knowledge of the anatomy of the Ordovician vertebrates indicates that the Australian and Bolivian forms are more closely related to each other, forming a monophyletic group (Arandaspidiformes), than to the North American genera which are more closely related to the heterostracans. The Ordovician vertebrates may thus be united with the heterostracans into a monophyletic group, the Pteraspidomorphi. This does not invalidate the myopterygian concept, but reduces the importance of the involved characteristics. The analysis suggests that the presence of two olfactory capsules is primitive for vertebrates, as is also a single median narial opening.