A group of mainly Cretaceous areoligeracean dinoflagellate cyst genera, which we call the ‘Cyclonephelium group’, has proved difficult to classify. The group comprises Aptea, Canningia, Canninginopsis, Cassidium, Cauveridinium, Cerbia, Circulodinium, Cyclonephelium, Doidyx, Senoniasphaera and Tenua. As a group, they also converge morphologically with ceratiaceans. Cyclonephelium-group taxa show considerable morphological diversity and gradation. However, the most important criteria for discriminating dinoflagellate cyst-based genera – tabulation and archaeopyle type – are uniform among areoligeraceans and ceratiaceans and so are not useful in this case. Any subdivision of the Cyclonephelium group will break apparently natural continuities; nevertheless, any resolution must involve a hierarchy of morphological criteria. In developing a ‘best-fit’ hierarchy of morphological criteria for the Cyclonephelium group and its separation from ceratiaceans, we consider historical concepts, morphological variation, illustrations in the literature (especially of types) and taxonomic stability. We conclude that the most pragmatic distinguishing feature of ceratiaceans in contrast to the Cyclonephelium group (and areoligeraceans in general) is that the former possess a lateral horn or distinct prominence on the inner body or wall. The hierarchy we favour within the Cyclonephelium group (in decreasing importance) is: (i) wall structure; (ii) whether the ornament is linear or free standing; and (iii) the distribution of the ornament. As a consequence, we propose one new genus (Trimuridinium), one new species (Aptea cassis), two new names (Canningia glomerata for Senoniasphaera rotundata and Circulodinium vectensis for Pseudoceratium distinctum), 49 new combinations and one new status. We emend the descriptions/diagnoses of Aptea, Circulodinium, Cyclonephelium, Pseudoceratium, Senoniasphaera, Tenua and Tenua hystrix. Cyclonephelium-group taxa predominate in neritic marine palaeoenvironments, and their use in palaeoecological analyses should be improved by a more cohesive and consistent taxonomy. The group may have been the root stock for ceratiaceans in the Late Jurassic, the two families becoming more clearly separate from the Late Cretaceous onwards. Cyclonephelium-group areoligeraceans are sparse in the Paleogene and confirmed species are absent in the Neogene.