It has been suggested that many arctic-alpine plant species have limited dispersal ability and cannot have arrived in Scandinavia and the arctic archipelago of Svalbard by long-distance dispersal after a total glaciation. It has therefore been proposed that such species must have survived the entire glaciation(s) in ice-free refugia in southern Norway, northern Norway and Svalbard. We investigated random amplified polymorphic DNA (RAPD) variation among 28 populations from Norway and Svalbard of one of these arctic-alpine ‘short-distance dispersers’, the selfing polyploid Saxifraga cespitosa. In an analysis of molecular variance (AMOVA), more variation was found among populations within the three postulated refugia regions (45%) than among these regions (25%). Spatial autocorrelation (Mantel) analyses showed that the genetic distance monotonously increased with increasing geographical distance. In UPGMA and PCO analyses, the populations from Norway and Svalbard formed a south–north cline that continued across the Barents Sea barrier. The results suggest that there has been recent dispersal among the three postulated refugia regions and thus that postglacial dispersal into these refugia regions from other distant areas also must represent a possibility. The observed geographical pattern of the genetic variation may have been established after expansion from different source areas outside the North European ice sheet and/or from different refugia areas ‘within’ the ice sheet, but it is probably not possible to distinguish among these alternatives. The results for S. cespitosa are consistent with a dynamic late- and postglacial scenario with extensive plant dispersal, and support the conclusion from our previous study of the outbreeding Saxifraga oppositifolia; the hypothesis of glacial survival in Norway and/or Svalbard is superfluous.