This thesis is primarily concerned with the application of numerical methods of taxonomic analysis to some Silesian goniatite assemblages. The taxa investigated here have been regarded in the past as belonging to the families Homoceratidae, Reticuloceratidae and Gastrioceratidae, plus the genus Homoceratoides. These are studied throughout their range, which is from the base of the Chokierian stage, Namurian, to the base of Westphalian C. British faunas are concentrated upon, but it is also of interest to investigate relationships with overseas faunas. The history of research into Silesian goniatites is discussed, and a brief account is given of the geological background to the subject, from which the precise difficulties and points of interest become apparent. The various taxonomic techniques which have been and are used in palaeontology are critically examined, and it is concluded that orthodox methodologies are inadequate for the present task. The statistical technique of cluster analysiS is, however, found to be suitable, and a new system of taxonomic analysis of goniatites is developed, based on phenetics. Methods of arriving at objective morphospecific divisions, higher taxonomic divisions, specimen determinations and phylogenies are devised and described. These techniques are then applied to data collected from the various goniatite faunas, and a complete and new systematic scheme is derived. British morphospecies are redescribed and all relevant genera have required redefinition. A new genus is described (Otleyoceras), and new species are described of Homoceras, Vallites, Homoceratoides, Otleyoceras, Bilinguites, Cancelloceras, Agastrioceras and Gastrioceras. The variation within faunas is described graphically and is found to have parallels with diverse other ammonoid groups. The mode of evolution is discussed, although the evidence is found to be ambiguous. and speculative phylogenies are proposed. Finally. some examples are given of how numerical analYSis can be useful in biostratigraphy.