Given the ongoing global accumulation of invasive species, it becomes crucial to better understand interactions among multiple alien species. Our experimental study, measuring growth, seed production and functional traits in 190 alien plant species combinations, shows that alien interactions are driven by hierarchical differences in functional traits reflecting competitive ability. While competition among two invaders was more prevalent, interspecific facilitation occurred in a quarter of cases, which could potentially exacerbate impacts on native species ('invasional meltdown'). Our findings advance the understanding of trait-interaction relationships, particularly by being applied to the novel case of alien-alien interactions. Synthesis Multiple invaders commonly co-occur in native ecosystems and in some cases have been shown to facilitate each other thus exacerbating impacts on native species, while in other cases one invader may reduce the impact of another due to competition. We therefore aimed at identifying mechanisms driving alien species interactions. We conducted a common garden experiment investigating all pairwise combinations of 20 alien annual plant species in Germany. We first tested whether competition or facilitation occurred more often. Secondly, we determined whether individual traits, hierarchical or absolute trait distances, multivariate trait or phylogenetic distance explained alien plant interactions best. Thirdly, we assessed whether accounting for trait plasticity explains plant performance better than species-level trait averages. While the magnitude of interspecific competition compared to intraspecific competition was on average larger across the 190 alien species combinations, interspecific facilitation still occurred in 24% of cases. Interactions could be better explained by hierarchical trait distances which reflect competitive ability, compared to phylogenetic and multivariate trait distance (reflecting niche differences). This finding supports criticisms about the applicability of testing limiting similarity versus environmental filtering and the community phylogenetic approach. Specifically, when growing taller and having a lower specific leaf area than the co-occurring alien neighbour, biomass and seed number of individuals in mixture increased compared to growing alone. Effects of seed mass, root:shoot ratio and flowering time depended on the performance measure. In contrast to recent suggestions, accounting for trait plasticity did not necessarily explain plant performance better than models using species-level trait averages. These results advance our fundamental understanding of trait-interaction relationships, strengthening recent findings on the importance of competitive hierarchy in shaping interactions and community structure. In particular, applying these concepts to the novel case of alien-alien interactions, is crucial given the continuing accumulation of alien species around the globe.