A new dinoflagellate cyst genus, Stoveracysta, is proposed to accomodate forms superficially resembling Alisocysta but differing in having a sexiform rather than a quinqueform hypocystal plate topology. The type species, Stoveracysta kakanuiensis sp. nov., is described from the upper Eocene/lower Oligocene boundary sequence exposed at Kakanui River mouth, south of Oamaru, New Zealand. The new combination S. (formerly Eisenackia and Alisocysta) ornata (Cookson & Eisenack 1965) is proposed. Both species may occur widely throughout the southern hemisphere but appear to be confined to a narrow stratigraphic interval, close to the Eocene/Oligocene boundary.