In the first few decades of this century, scientists working on the genetics of bryophytes mosses and liverworts were at the forefront of genetical research: Allen (1917) was the first to describe sex chromosomes in plants, Heitz (1928) demonstrated the continuity of chromosomes during the mitotic cell cycle, and Knapp (1936) employed X-ray mutagenesis for genetical research. Although the beginning of plant molecular genetics was marked by ultraviolet light (UV) mutagenesis of the liverwort Sphaerocarpos donellii, which demonstrated DNA as the molecular basis of inheritance (Knapp et al. 1939), bryophytes have only been of marginal interest for modern molecular biologists. The outstanding exception is the liverwort Marchantia polymorpha, which was first subjected to genetical analysis with intensive mutation and cross-breeding experiments (Burgeff 1943). It is now well known because complete nucleotide sequences have been determined for its plastid and its mitochondrial DNA (Ohyama et al. 1986; Oda et al. 1992). Non-mendelian inheritance was first postulated by von Wettstein (1928) who analysed Funaria hygrometri ca and related mosses. Likewise, von Wettstein (1924) recognised the great potential of the haploid moss protonemata for genetically dissecting differentiation processes. These analyses started with mutant induction in Physcomitrium piriforme, Funaria hygrometrica and Physcomitrella patens (Barthelmes 1940; Oehlkers and Bopp 1957; Engel 1968) and culminated in the synopses