Having spent many years in working through the Cretaceous Cribrimorph material in the British Museum, and, consequently, the literature of the subject, I was forced to the conclusion that various Cribrimorph stocks had independently arisen over and over again from Membranimorph ancestors, had run through a more or less similar evolution, and, finally, become extinct; so that the many forms described under Cribrilina, Membraniporella , and other Recent genera were really in no way closely related to these, and the Cretaceous Cribrimorph forms, in consequence, needed at lea st a generic nomenclature of their own. These Cretaceous forms fell under ten main stocks, between which no direct relationship could be discovered, and whose common ancestor must be sought far back among the primitive Membranimorphs; so that it did not seem too much to claim for each of these main stocks the status of a family. Within certain families were several well-defined groups, which, nevertheless, in each case had features in common, rendering it possible for all to have been derived from a common Cribrimorph ancestor; it seem ed permissible, therefore, to regard these groups as subfamilies. Thus a complete evolutionary classification was drawn up for the Cretaceous Cribrimorphs, and this, in the tersest possible form, was published in the ‘Annals and Magazine of Natural History (Lang, 1916). Since the whole evolutionary scheme was implicit in the tabular analysis, it was hoped that this would be lucid enough to be acceptable without further explanation. From, various criticisms, it appears that this is not so, and the opportunity has been taken in this essay to select one subfamily and expand the condensed account into a fuller statement. The subfamily Pelmatoporinæ was chosen partly because of its large size, and partly because it illustrates so fully the principles of evolution exhibited by the Cretaceous Cribrimorphs generally; but other subfamilies would serve the same purpose nearly as well. The morphology of the group is the first consideration; and since it is founded on the structure of the species Pelmatopora calceata , which closely approximates to the supposed ancestral form, this radical species is considered in some detail. Then, after examining the evolutionary aim of Cretaceous Cribrimorphs as a whole, we are in a position to appreciate the general evolutionary history of each character of the radical species, as it proceeds from the less to the more complex forms in the several lineages. Next, peculiar modifications of certain characters are described, giving the criteria for generic distinctions; then the evolution of forms within each genus. The results are compared with those obtained by W. K. Spencer in his work on Cretaceous Asteroidea. Next, the stratigraphical distribution of the forms is examined to see how far this corroborates the relationships established on morphic evidence; and, finally, the evidence of recapitulation, as shown in the colonial development (Astogeny), is brought to bear in connection with the other two criteria of relationships already examined.