||The spiracular region, comprising the hyomandibular pouch together with the mandibular and hyoid arches, has a complex evolutionary history. In living vertebrates, the embryonic hyomandibular pouch may disappear in the adult, develop into a small opening between the palatoquadrate and hyomandibula containing a single gill-like pseudobranch, or create a middle ear cavity, but it never develops into a fully formed gill with two hemibranchs. The belief that a complete spiracular gill must be the ancestral condition led some 20th century researchers to search for such a gill between the mandibular and hyoid arches in early jawed vertebrates. This hypothesized ancestral state was named the aphetohyoidean condition, but so far it has not been verified in any fossil; supposed examples, such as in the acanthodian Acanthodes and symmoriid chondrichthyans, have been reinterpreted and discounted. Here we present the first confirmed example of a complete spiracular gill in any vertebrate, in the galeaspid (jawless stem gnathostome) Shuyu. Comparisons with two other groups of jawless stem gnathostomes, osteostracans and heterostracans, indicate that they also probably possessed full-sized spiracular gills and that this condition may thus be primitive for the gnathostome stem group. This contrasts with the living jawless cyclostomes, in which the mandibular and hyoid arches are strongly modified and the hyomandibular pouch is lost in the adult. While no truly aphetohyoidean spiracular gill has been found in any jawed vertebrate, the recently reported presence in acanthodians of two pseudobranchs suggests a two-step evolutionary process whereby initial miniaturization of the spiracular gill was followed, independently in chondrichthyans and osteichthyans, by the loss of the anterior pseudobranch. On the basis of these findings we present an overview of spiracular evolution among vertebrates.