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ABSTRACT Aim Determining which traits predispose a species to become invasive is a fundamental question of invasion ecology, but traits affect invasiveness in concert with other factors that need to be controlled for. Here, we explore the relative effects of biological traits of plant species and their distributional characteristics in the native range on invasion success at two stages of invasion. Location Czech Republic (for native species); and the world (for alien species). Methods The source pool of 1218 species of seed plants native to Central Europe was derived from the flora of the Czech Republic, and their occurrence in 706 alien floras all over the world was recorded, distinguishing whether they were listed as an 'alien' or a 'weed' in the latest version of Randall's 'Global compendium of weeds' database. The latter type of occurrence was considered to indicate species ability to invade and cause economic impact, i.e. a more advanced stage of invasion. Using the statistical technique of regression trees, we tested whether 19 biological traits and five distributional characteristics of the species in their native range can be used to predict species success in two stages of invasion. Results The probability of a species becoming alien outside its native distribution range is determined by the size of its native range, and its tolerance of a wide range of climates acquired in the region of origin. Biological traits play only an indirect role at this stage of invasion via determining the size of the native range. However, the ability of species to become a weed is determined not only by the above characteristics of native distribution, but also directly by biological traits (life form and strategy, early flowering, tall stature, generative reproduction, number of ploidy levels and opportunistic dispersal by a number of vectors). Species phylogenetic relatedness plays only a minor role; it is more important at the lowest taxonomic levels and at the later stage of invasion. Main conclusion The global success of Central European species as 'weeds' is determined by their distributional characteristics in the native ranges and by biological traits, but the relative importance of these determinants depends on the stage of invasion. Species which have large native ranges and are common within these ranges should be paid increased attention upon introductions, and the above biological traits should be taken into account in screening systems applied to evaluate deliberate introductions of alien plants to new regions