On the basis of electron microscopy of dry whole mounts of wild material set up in situ mainly in the Galapagos Islands but with two introductory specimens from South Africa, the presence of unmineralized periplast components has been demonstrated in two genera of fully calcified coccolithophorids (Ophiaster and Calciopappus) and also in a broken cell, otherwise attributable to Chrysochromulina aff. fragilis Leadbeater. The last possesses many small elliptical plate scales with characteristic surface markings, together with fewer but larger sheet scales, each membranous, flexible, and almost without patterning except at the edge which carries a narrow zone of sparse radial striations. Both types of scale recur in the two coccolithophorid genera, the small elliptical plates as an underlayer beneath the coccoliths and the peripherally streaked membranes individually attached to the proximal surfaces of coccoliths as an integral part of their structure. Though present, these are more difficult to detect in Calciopappus than in Ophiaster in which they have been clearly demonstrated in specimens from both South Africa and the Galapagos Islands. In addition, some types of Ophiaster have also been shown to possess completely patternless membranes, detectable only by their indirect effects, occupying the apparently vacant plate centres of coccoliths in special positions. Other aspects of coccolith substructure are discussed with special reference to recurring difficulties regarding speciation in the two genera. Revised generic descriptions are provided but specific descriptions are limited to Ophiaster. These include revision of the two existing taxa (especially necessary for `O. formosus Gran') and the erection of three additional new taxa (O. reductus sp.nov., O. minimus sp.nov. and O. formosus var. inversus var.nov.). The final discussion summarizes and comments on present knowledge of Chrysochromulina fragilis sens. lat. in relation to several genera of coccolithophorids including, but not limited to, Ophiaster and Calciopappus.