1 A study of allozyme variation in vegetatively propagating populations of the rhizomatous sedge Carex bigelowii, revealed high levels of clonal diversity (genet diversity) within populations. The structure of allelic variation within the populations suggests that sexual reproduction has played a significant role in these C. bigelowii populations, despite present lack of seedling recruitment. The study was carried out in moss-heath communities on Icelandic lava-fields. Two adjacent populations were studied at one site, while a third population was studied at a second site, 35 km away from the first two populations. 2 The number of genets detected in each population, among 85-88 analysed ramets, ranged from 41 to 55 (minimum estimate). Samples were taken every 4 m along transects in the populations. Ramets with the same allozyme genotype were often spatially aggregated. No seedlings have been observed in the populations during five years of demographic studies. 3 All the populations studied showed a diploid expression of allozymes and high levels of allelic variation, with on average 491.77 alleles per locus (A) and an allelic diversity (HS) of 0.167. Similar levels of within-population variability are found in many wind-pollinated and outcrossing plant species. 4 The difference between observed and expected heterozygosity was small in all populations, suggesting high levels of outbreeding. 5 Comparisons with other Carex taxa show that the levels of and structuring of allozyme diversity in C. bigelowii is similar to that in other outbreeding species (usually rhizomatous), and much higher than in inbreeding species (which are usually caespitose). 6 Only 5the total allelic diversity was explained by differences between the two study sites (G ST = 0.055), suggesting extensive recent or historic gene-flow.