An elevated skeletal structure surrounding an empty axial area occurs in many unrelated taxa within the Rugosa. This structure, commonly termed the aulos, was first differentiated and described by Grabau in 1922. Most terms introduced by that author for individual morphotypes have not been accepted because the taxa he chose to illustrate the typical development do not correspond to his diagnoses. The morphogenetic study on some circumaxial structures in this paper points out differences in their origin, their predicted role in the physiology of the coral polyps. The study shows both the advantages and disadvantages of the use of these circumaxial structures in taxonomy. In addition to the term aulos, which was introduced by Smith in 1928, new terms i.e. circulotheca and columnotheca are here introduced for the circumaxial structures that also are newly proposed names, to allow distinguishing them from true axial structures.