The relationships between ·66 representative pleurocarpous mosses were studied using cladistic analyses. Ten different analyses were perfoqned with different outgroups or single taxa deleted to check the stability of the analyses (all resulted in too manYl!ees for other tests· of stability to be applicable). Another three analyses were performed with different sets of characters excluded to see if some kinds of characters were more important than the others for the results of the analyses. The study suggests that the Fleischer-Brotherus system has support for large parts of the classification, although the order Isobryales (Leucodontales), in the sense of Brotherus, is a grade taxon. More recent ideas about the classification of the Isobryales, which are partly based on the differences between perfect and reduced peristomes, are not supported. Jmportant and relatively stable clades are formed by (1) the species of the Amblystegiaceae (s.l.) plu~Thaidium and some members of the Hypnaceae, (2) the members of the Plagiotheciaceae (in a relatively wide sense) and (3) the Hookeriales-Sematophyllaceae-Garovagliodeae.Two of the analyses indicate that the last clade may be related t?·the Ptychomniaceae. The families· Brachytheciaceae, Hypnaceae and Thuidiaceae, in their usual sense, appear to be polyphyletic. Characters of the sporophyte and perichaetia were in general more important for the results of the analyses than characters of the vegetative gametophyte, due to their more consistent patterns of variation among the taxa. However, in some cases, such as the definition of the Plagiotheciaceae clade, vegetative gametophytic features proved to be more important than other characters.