In several recently published phylogenetic analyses, two Lower Devonian taxa, Doliodus and Pucapampella, both fall on the chondrichthyan stem, very close to the base of ‘conventionally defined chondrichthyans’ (i.e., forms possessing tessellated mineralization of the cartilaginous endoskeleton). These two taxa nevertheless exhibit strongly discordant morphologies from each other. A summary of the anatomical data concerning these taxa is presented here, including new, as well as previously published, findings. A new family Pucapampellidae is erected, containing Pucapampella and a newly recognized genus from South Africa. Morphological evidence is summarized for the monophyly of crown elasmobranchs (sharks and rays), holocephalans (chimaeras) and other chondrichthyans. Based on these data, Doliodus and pucapampellids both fall outside the chondrichthyan crown, but their relative phylogenetic positions on the chondrichthyan stem are unclear. Pucapampellid interrelationships are particularly hard to assess because little is known beyond their cranial and visceral arch morphology and also because pucapampellids possess a suite of ontogenetically primitive (and thus potentially neotenic) features. By contrast, the phylogenetic position of Doliodus seems less elusive; it possessed an ‘acanthodian-like’ complex of dermal spines, including pectoral fin spines, prepectoral, admedian, and prepelvic spines, and possibly dorsal and pelvic fin spines, in conjunction with numerous ‘chondrichthyan-like’ endoskeletal features and a heterodont ‘sharklike’ dentition. Doliodus can be viewed as a quintessential component of the evolutionary transition between ‘acanthodians’ and ‘conventionally defined chondrichthyans’, leaving little doubt that the chondrichthyan total group includes ‘acanthodians’ (now widely perceived to be a paraphyletic group, populating the basal part of the chondrichthyan stem). Although Doliodus has been resolved as a basal member of the ‘conventionally defined chondrichthyans’, it could occupy a more basal position on the chondrichthyan stem.