Invasion ecology tends to treat taxonomic groups separately. However, given that all invasive species go through the same stages of the invasion process (transport, escape, establishment, spread), it is likely that – across taxa – comparable traits help to successfully complete this process ("invasion traits"). Perhaps not all invasive species have the same invasion traits, but different combinations of invasion traits can be found among invaders, corresponding to different possibilities to become a successful invader. These combinations of invasion traits might be linked to taxonomic affiliation, but this is not necessarily the case. We created a global dataset with 201 invasive species from seven major taxonomic groups (animals, green plants, fungi, heterokonts, bacteria, red algae, alveolates) and 13 invasion traits that are applicable across all taxa. The dataset was analysed with cluster analysis to search for similarities in combinations of invasion traits. Three of the five clusters, comprising 60% of all species, contain several major taxonomic groups. While some invasion trait frequencies were significantly related to taxonomic affiliation, the results show that invasive species from different taxonomic groups often share similar combinations of invasion traits. A post-hoc analysis suggests that combinations of traits characterizing successful invaders can be associated with invasion stages across taxa. Our findings suggest that there are no universal invasion traits which could explain the invasion success of all invaders, but that invaders are successful for different reasons which are represented by different combinations of invasion traits across taxonomic groups.