Summary1. Different grass species dominate grasslands fertilized with nitrogen (N) or phosphorus (P), possibly due to the impact of N : P stoichiometry on competitive interactions. How species compete for nutrients, and whether the mechanisms are similar for N and P, is still not fully understood.2. We investigated whether the outcome of competition between Alopecurus pratensis and Agrostis capillaris depends on N : P stoichiometry, and on the ability to acquire supplied N or P. Monocultures and mixtures of the two species were grown in pots at nine combinations of N and P supply (N : P ratios 1·7, 15 and 135, all at three supply levels). After 3 months, we determined plant biomass, morphological traits and nutrient concentrations of plant tissues.3. N : P supply ratios had similar effects on the growth of the two species but contrasting effects on their competitive strength, as assessed by comparing growth in competition to growth in monoculture: Alopecurus was the stronger competitor under N limitation (N : P ratio 1·7), whereas Agrostis was an equal or stronger competitor under P limitation (N : P ratio 135). This result resembled patterns of species distribution observed in the field.4. The strong competitive response of Alopecurus at the low N : P supply ratio was associated with a high investment in root biomass and root length, and a high nitrogen productivity. The competitive response of Agrostis at the high N : P supply ratio was associated with low root mortality and high root phosphatase activity.5. Our results obtained under N limitation support the pre-emption theory in which plants with the highest root length are able to acquire more N from the soil than their competitors, and therefore can suppress their growth. Under P limitation, however, plant investment in root length could not explain competitor suppression. Here, other factors important in competition for P, such as mycorrhizal hyphal length, root longevity, or exudation rates of P releasing compounds, merit investigation.