AbstractRecent empirical advances in bryophyte systematics have been made in the discovery and detailed study of new characters. However, theoretical considerations have not kept pace. Proper attention has not been paid to how these new characters can be used to discover relationships among groups and produce classifications. Recent cladistic studies of the relationships of the major groups of bryophytes have demonstrated the feasibility and usefulness of an approach to phylogenetic systematics derived from the works of Hennig. A Hennigian approach attempts to find the particular hierarchical level at which a given character is a homology (i.e. a synapomorphy or shared, derived character), relationships are established by searching for congruent patterns of homologies, and the resulting hierarchical scheme is used as the basis for a classification. Such an approach provides a rigorous and explicit logic for investigating phylogeny and recognizing natural, historically discrete taxa. The theoretical advantages of a Hennigian approach are discussed and illustrated by examining the congruence of new characters data with preliminary cladograms of the major bryophyte groups.