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Background †Saurichthyiformes were a successful group of latest Permian–Middle Jurassic predatory actinopterygian fishes and constituted important, widely-distributed components of Triassic marine and freshwater faunas. Their systematic affinities have long been debated, with †saurichthyiforms often being aligned with chondrosteans, a group today comprising sturgeons and paddlefishes. However, their character-rich endocranial anatomy has not been investigated in detail since the first half of the 20th century. Since then, major advances have occurred in terms of our understanding of early actinopterygian anatomy, as well as techniques for extracting morphological data from fossils. Results We used μCT to study the internal cranial anatomy of two of the stratigraphically oldest representatives of †Saurichthys, from the Early Triassic of East Greenland and Nepal. Our work revealed numerous previously unknown characters (e.g., cryptic oticooccipital fissure; intramural diverticula of braincase; nasobasal canals; lateral cranial canal; fused dermohyal), and permitted the reevalution of features relating to the structure of cranial fossae, basicranial circulation and opercular anatomy of the genus. Critically, we reinterpret the former †saurichthyiform opercle as an expanded subopercle. For comparison, we also produced the first digital models of a braincase and endocast of a sturgeon (A. brevirostrum). New information from these taxa was included in a broad phylogenetic analysis of Actinopterygii. †Saurichthyiforms are resolved as close relatives of †Birgeria, forming a clade that constitutes the immediate sister group of crown actinopterygians. However, these and other divergences near the actinopterygian crown node are weakly supported. Conclusions Our phylogeny disagrees with the historically prevalent hypothesis favoring the chondrostean affinities of †saurichthyiforms. Previously-proposed synapomorphies uniting the two clades, such as the closure of the oticooccipital fissure, the posterior extension of the parasphenoid, and the absence of an opercular process, are all widespread amongst actinopterygians. Others, like those relating to basicranial circulation, are found to be based on erroneous interpretations. Our work renders the †saurichthyiform character complex adequately understood, and permits detailed comparisons with other stem and crown actinopterygians. Our phylogenetic scheme highlights outstanding questions concerning the affinity of many early actinopterygians, such as the Paleozoic–early Mesozoic deep-bodied forms, which are largely caused by lack of endoskeletal data. Electronic supplementary material The online version of this article (10.1186/s12862-018-1264-4) contains supplementary material, which is available to authorized users.