It is classically known that the oldest representatives of vertebrates are Ordovician, heterostracan-like, dermal bone-bearing animals from Australia and North America. Another taxon, phylogenetically related to one of the Australian species, has recently been discovered in the Ordovician of Bolivia. However other discoveries of Lower Palaeozoic fossils shed a new light on the oldest representatives of primitive chordates (urochordates, cephalochordates). Most recent publications on this topic are reviewed. Anatolepis is rejected from chordate affinities. Euconodonts, more and more often cited as myxinoid (hagfish) relatives, are considered with doubt. A phylogenetic scheme is suggested, constrained by the stratigraphic record, and the minimum age of appearance of the main taxa is proposed : chordates in Early Cambrian times, vertebrates in mid-Ordovician times.