This thesis describes a study of six North American, dioicous Brachytheeium species possessing a rough seta. The phenetic variability of the six species was analysed in order to clarify the relationships, between species and to provide .simpler, more reliable means of identifying specimens. As a consequence of this investigation, the taxonomic identities of B. asperrimum (Mitt. ex. C. Muell.) Sull. and B. frigidum (C. Muell.) Besch, have been established through numerical analyses of the variation in the gametophytic features of the two species. Two types of analyses were used: a principal components analysis and a cluster analysis. The phenetic variation and habitat specificity of each species were analysed and documented and synonymy and ranges presented. A. test of the features considered diagnostic for the two species has been performed and the results of this test used to devise a reliable key. The relationships of the two species to the other North American dioicous species possessing rough setae were determined using a principal components analysis and. a cluster analysis. B. asperrimum (Mitt. ex. C. Muell.). Sull is shown to be closely related to B. bolanderi (Lesq.) Jaeg. and Sauerb.. B. frigidum (C. Muell.) Besch. is shown to be closely related to B. rivulare B.S.G. and B. nelsonii Grout. A dendrogram and discussion of the hypothetical, cladistic relationships of the six species are provided. / Science, Faculty of / Botany, Department of / Graduate