The subgenus Anaskopora Wass,1975 is raised to generic rank, separated from the genus Corbulipora, and redefined. The type species, Cribrilina elevata MacGillivray, 1895, is a Tertiary fossil from Victoria with small globular colonies formed principally by a special kind of interzooidal frontal budding. Other Tertiary fossil species with a similar colony structure, here assigned to Anaskopora, are Cribrilina cornuta MacGillivray, 1895 and Lepralia rotundata MacGillivray, 1895. Two further new Tertiary species, A. simplex and A. mesa, from Victoria and South Australia have small encrusting colonies. A key to species is given.