This is the first monograph, which summarizes the data on cyclomorphosis of the Heliolitida. The characteristics of the manifestation of cyclomorphosis at the intracolonial and population levels and within the phylums are considered. Reworking of the concept "phylum" is given. It is shown that a change in the growth rate of populations could lead to the emergence of new taxa. The conditions under which recapitulations could be restored have been clarified. The difference between the acceleration of growth and accelerated development is explained. The question of the relationship between cyclomorphosis and the duration of the evolution of phylums is considered. Data on cyclomorphosis of other groups of coelenterates are brought. The work is intended for paleontologists and biologists interested in morphology, evolution and systematics of Paleozoic corals and biorhythmology. It can also be useful to graduate students and students of biological specialties.