The cateniform tabulate corals Halysites and Cystihalysites have normal corallites and an intercorallite coenosteum of tubules or dissepimental tissue (the mesocorallites or microcorallites of most earlier workers). Study of several specimens, chiefly from the Silurian of Gotland, reveals that the two genera exhibit markedly different patterns of lateral and interstitial increase. In lateral increase of Cystihalysites, corallites and intercorallite dissepimental tissue develop alternately along the base of a new rank. On the other hand, the corallites of Halysites occur along the bottom of the new rank with intercorallite tubules inserted above the base. In interstitial increase of Cystihalysites the intercorallite tissue is vertically continuous, bifurcating to either side of the newly-formed corallite. In contrast, there is a gap in the vertical continuity of intercorallite tissue in Halysites. A tubule is replaced by a new corallite; then at a higher level, two new tubules become inserted to either side of the new corallite. Differing interpretations of the manner of development of both lateral and interstitial increase in Halysites depend on whether the polyps originally lived in shallow or deep calices.