On the basis of a research started about 40 years ago for the knowledge of the internal structure and mode of growth of the Larcoidea Radiolaria, this article discusses and describes a series of genera and species of larnacillid radiolarians from two subfamilies: Cryptolarnaciinae and Circodiscinae. Ten genera are discussed, of which 6 are new (Phacolarnacium, Globolarnacium, Pylolarnacium, Sanfiriedellus, Circodiscullus, and Stylotrochellus), and 29 species are discussed, of which 17 are described as new. For all of them have been made sections to know as well as possible their initial structure as base of taxonomy. Special illustrations are presented to suggest horizontal gene transfer for at least one species. A partly changed nomenclature of the structural elements of the microsphere and initial skeleton of these radiolarians is proposed.