The "Treatise" Hyalospongea of de Laubenfels need division into separate classes Hexactinellida and Heteractinida. The Heteractinida appear to be allied to the Demospongia if to any living sponges. The name Hexactinellida does not imply a diagnosis hinging on the presence of hexactins; the diagnostic character implied is a spicular system which is wholly triaxial in basis, with the triaxial hexactin as its central type of spicule. Neither of the 2 other classes of siliceous sponges (Demospongia, Heteractinida) has a spicular system of this character, and those of both include types of spicules which are not triaxial and are not found in Hexactinellida. The Hexactinellida are also distinguished from other modern sponges (Calcarea, Demospongia) by the nature of their soft parts; there are no grounds for thinking that the same type of soft parts were present in the Heteractinida. The concept of a taxon Hyalospongiae due to Claus was not based on any criterion which defines any class of Porifera, and part of its basis was imaginary. Union of spicules by fusion is not general in Hexactinellida, but is known from only 1 of 2 sub-classes (Hexasterophora). The names "glass-sponge" and Hyalospongiae (-ea) are misleading, because glassiness of the spicules is no more typical of the Hexactinellida than of the Demospongia. "Hexactinellidae Schmidt, 1870" must not be treated as a family name based on that of the genus Hexactinella Carter, 1883.