Thirty-seven superfamilies of Lamellibranchia (predominantly suspension-feeding) were graded according to their overall more primitive or more advanced structural condition, by tabulation based on two organ systems exhibiting progressive series of character-states (ctenidia, marginal pallial fusion). Commencing with the more primitive superfamilies, these were investigated in groups, recording the occurrence of those character-states that were especially relevant to the group in question. By this means the superfamilies were arranged in five clusters, and the structural characteristics of each cluster were clearly reported. By these methods, and together with three superfamilies of Protobranchia, the Bivalvia are shown to comprise six clusters which have been arranged in the following classificatory system. Subclass 1 Protobranchia Order 1 Nuculoida Order 2 Solemyoida Subclass 2 Lamellibranchia Order 3 Pteriomorpha Order 4 Mesosyntheta Suborder Trigonioida Suborder Unionoida Order 5 Anomalodesmata Suborder Pholadomyoida Suborder Septibranchia Order 6 Gastropempta Suborder Veneroida Suborder Myoida This classification is in general agreement with that adopted in the Treatise on invertebrate palaeontology (ed. R. C. Moore, University of Kansas Press, 1969-71) save for the following points. (i) Four subclasses are suppressed, reasons given. (ii) The superfamilies Crassatellacea, Carditacea and Leptonacea are transferred out of the Veneroida to join the Unionacea in an expanded suborder Unionoida. This improved classification differs in a few respects from the taxonomic arrangement previously obtained by computer analysis (R. D. Purchon, Phil. Trans. R. Soc. Lond. B 284, 425-436 (1978)) owing to additional information, and to more sensitive methods of analysis. The methods used provide clear reasons for the classification adopted, and permit easy adjustments to the classification if these are required after incorporation of any new information that may become available. The principal attributes of the nuculoid protobranchs and of the subclass Lamellibranchia are compared and contrasted in tabular form. A diagram, incorporating four hypothetical ancestral stages, illustrates the probable course of evolution in the class Bivalvia. An appendix supplies five further tabulations demonstrating the relevance to classification of the structural variation within certain of the organ systems. Throughout these six tabulations a majority of the superfamilies exhibit uniformity in their associations.