Input from molecular phylogenetics in the past five years has substantially altered concepts of systematic relationships among liverworts. While these studies have confirmed the monophyly of phylum Marchantiophyta, they have demonstrated that many previously recognised ranks within the hierarchy are unnatural and in need of modification. Changes in the ranks of suborder and above have been proposed by various workers, but modifications in the circumscription of genera and families are still required. A comprehensive, phylogenetic classification scheme that integrates morphological data with molecular hypotheses is presented. The scheme includes diagnoses and publication citations for all names above the rank of genus. All currently recognised genera are listed alphabetically in their respective families; subfamilies are not indicated. Major modifications and novel alignments of taxa are thoroughly discussed, with pertinent references provided. Jungermanniaceae is redefined and Solenostomataceae fam. nov. is formally described to accommodate some of the genera excluded from it.

A pair of coupled nonlinear differential equations is studied and asymptotic properties of its non-oscillatory solutions are obtained. In particular, we provide classification schemes for these solutions which are justified by existence criteria.