Following the discovery of several body fossils in Scotland and South Africa, most paleontologists think conodonts — which turn out to have fins, cheveron shaped muscles, and eyes — are in the phylum chordata. There are a lot of opinions about where the conodonts belong amongst the chordates/vertebrates. Some paleontologists (Cochrane) place the Protoconodonts (therefore possibly also the conodonts) in a phylum along with the chaetognath worms.
A cladistic analysis by Donoghue et. al (1998). suggests that conodonts and Euconodonts are vertebrates. The paraconodonts (known only from teeth) are thought to be related, but the relationship is unclear. Per Donoghue, Paraconodonts are not related to the rest.
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