ABSTRACT Little is known about the traits and mechanisms that determine whether or not a species will be invasive. Invasive species are those that establish and spread after being introduced to a novel habitat. A number of previous studies have attempted to correlate specific plant traits with invasiveness. However, many such studies may be flawed because they fail to account for shared evolutionary history or fail to measure performance directly. It is also clear that performance is context dependent. Thus, an approach that corrects for relatedness and incorporates multiple experimental conditions will provide additional information on performance traits of invasive species. I use this approach with two or three pairs of invasive and closely related non-invasive species of Commelinaceae grown over experimental gradients of nutrient and water availability. Invasive species have been introduced, established, and spread outside their native range; non-invasive species have been introduced, possibly (but not necessarily) established, but are not known to have spread outside their native range. The invasive species had higher relative growth rates (RGR) than non-invasive congeners at high nutrient availabilities, but did not differ from non-invasive species at low nutrient availabilities. This is consistent with a strategy where these particular invasive species are able to rapidly use available resources. Relative growth rates were also higher for two out of three invasive species across a water availability gradient, but RGR did not differ in plasticity between the invasive and non-invasive species. This suggests that nutrient addition, but not changes in water availability, might favour invasion of dayflowers. This approach is novel in comparing multiple pairs of invasive and non-invasive congeners across multiple experimental conditions and allows evaluation of the robustness of performance differences. It also controls for some of the effects of relatedness that might confound multispecies comparisons.