The following species hare been studied: Polygonum lapathifolium L., P. nodosum Pers., P. persicaria L., P. hydropiper L., P. mite Schrank., P. minus Huds. In Section k the taxonomy of the species has been investigated. The species are often regarded as critical and plastic, and hybrids have been frequently recorded. Cultivation tinder different conditions and the scoring of natural populations are among the methods which have been used, and achene characters have been shown to be extremely useful. Herbarium material incltuSing the Linnean specimens has also been studied. Polygomim lapathifolium L. is regarded as the most critical species and suggestions are made with regard to the relationship of this species to P. nodosum Pers. and P. tomentosum Schrank. Hybridisation is shown to be very infrequent. In Section B the ecology of the species is recorded, including some experimental work, and it is clear that the morphological subdivision into Densiflorae and Laxiflorae is correlated with the ecology, the former being weed species and the latter non-weed species. In Section C the germination problems have been investigated. While in P. lapathifolium L. germination is possible after a few weeks, in P. persicaria L., P. mite Schrank., and P. minus Huds., the pericarp has to be partly removed before water can enter. In P. hydropiper L. in addition to an impermeable pericarp a slow biochemical reaction must also take place, the end product of which appears to be glucose. The effect of gibberellic acid has been studied and germination inhibitors have been shown to be present.