1. Changes in savanna tree species composition, both within landscapes and across climatic gradients, suggest that species differ in their ability to utilise resources and cope with grass competition. Linking trait variation among species to their relative performance under resource limitation and competition treatments could provide mechanistic understanding of species’ turnover across environmental gradients in savannas. We investigated how tree species differ in response to competition from grasses and nutrient supply, and whether these responses can be related to plant traits. As humid savannas are often associated with low fertility, species of humid savannas may grow more efficiently under nutrient suppression than species from semi-arid savannas. In heterogeneous grass swards, fast-growing, resource-wasteful species may be found in short-grass patches and slow-growing, resource-conservative species in tall-grass patches. 2. We compared seedlings of 40 tree species sampled from humid and semi-arid savannas of three continents (Africa, Australia, South America) with and without grass competition and with high and low nutrient supply. We measured traits related to soil resource capture, light capture and growth, and tested whether these traits were related to performance under the four treatments. 3. All tree species were suppressed by grass competition and most by nutrient limitation. Only species from humid savannas in Australia grew better under nutrient limitation than their semi-arid counterparts. Deciduous species from semi-arid climates were more negatively impacted by grass competition than deciduous species from humid climates whereas the reverse pattern was observed among evergreen species. Faster growing species were more severely suppressed by grass competition and low nutrients than slower growing species. Traits associated with soil resource capture and seed mass supported growth under grass competition and nutrient limitation, but the traits differed by continent and by leaf habit. 4. Synthesis: We found limited evidence that tree seedlings from humid savannas grow better under nutrient limitation than species of semi-arid savannas. We confirmed that fast-growing species may be advantaged in short-grass patches and conservative species may be advantaged in tall-grass patches. Traits that improved performance under grass competition differed by continent, which may relate to differences in leaf habit and constraints on seed size.