A new actinopterygian, Cuneognathus gardineri new genus and species, is described from the Devonian (Famennian) Obrutschew Bjerg Formation of East Greenland on the basis of multiple incomplete specimens. Cuneognathus most closely resembles Limnomis from the Famennian Catskill Formation of Pennsylvania, and, like that taxon, is known exclusively from freshwater deposits. A cladistic analysis with an ingroup of 13 actinopterygians and an outgroup of five sarcopterygians explores the relationships between the new genus and some of its better-known Devonian contemporaries, and recovers the same four topologies regardless of the implementation of limited character ordering. Cheirolepis is resolved as the most basal of well-known Devonian actinopterygians, consistent with a majority of previous studies. A novel sister-group relationship between Howqualepis and Tegeolepis is found in all trees. Disagreement between the most parsimonious cladograms is concentrated in a clade whose members are often informally referred to as ‘stegotrachelids.’ Cuneognathus and Limnomis are resolved as sister taxa within this large radiation along with the pairings of Moythomasia dugaringa plus M. nitida and Krasnoyarichthys plus Stegotrachelus. The arrangement of taxa is conserved when the enigmatic Dialipina is added to the analysis, although the reconstructed position of that genus above both Cheirolepis and Osorioichthys seems improbable. Our scheme of relationships suggests that actinopterygians invaded freshwater environments at least four times during the Devonian, while age constraints indicate that many of the cladogenic events between ingroup taxa included in this study occurred during or before the Givetian.