Almost all blastogeny in colonial rugose and tabulate corals involves lateral increase. Axial increase is rare and peripheral increase, which uncommonly occurs in both solitary and colonial corals, is regarded as a multiple type of rejuvenescence. Coenenchymal increase is known only in heliolitid corals. During lateral increase in fasciculate and massive colonies, offset and parent are separated by either a partition which is interpreted as formed by a continuous sheet of basal ectoderm between offset and parent polyps, or by a dividing wall which is formed by two entirely separate polyps. Lateral increase in species of Favistina and Palaeophyllum from the Upper Ordovician of eastern North America involves offsets which are separated from the parent coralIite by a dividing wall. Axial planes of the offsets are oriented towards the axis of parent corallites, with the counter septum located on the peripheral wall. Septal insertion in general shows a rugosan pattern. Tertiary septa are present in two specImens of Palaeophyllum.