Initial soil development and enhanced nutrient retention are often important underlying environmental factors during primary succession. We quantified the accumulation rates of nitrogen (N) and soil organic matter (SOM) in a 37-year-long chronosequence of Leymus arenarius dunes on the pristine volcanic island Surtsey in order to illuminate the spatiotemporal patterns in their build-up. The Leymus dune area, volume and height grew exponentially over time. Aboveground plant biomass, cover or number of shoots per unit area did not change significantly with time, but root biomass accumulated with time, giving a root / shoot ratio of 19. The dunes accumulated on average 6.6 kg N ha⁻¹ year⁻¹, which was 3.5 times more than is received annually by atmospheric deposition. The extensive root system of Leymus seems to effectively retain and accumulate a large part of the annual N deposition, not only deposition directly on the dunes but also from the adjacent unvegetated areas. SOM per unit area increased exponentially with dune age, but the accumulation of roots, aboveground biomass and SOM was more strongly linked to soil N than time: a 1 g m⁻² increase in soil N led on average to a 6 kg C m⁻² increase in biomass and SOM. The Leymus dunes, where most of the N has been accumulated, will therefore probably act as hot spots for further primary succession of flora and fauna on the tephra sands of Surtsey.