The successful spread of invasive plants may result from an evolutionary shift in resource allocation from defence to growth due to release from enemies, as proposed by the 'evolution of increased competitive ability' hypothesis (EICA). The crucifer Lepidium draba was used to test this hypothesis, measuring growth and levels of glucosinolates and myrosinase of leaves as constitutive defence parameters. Individuals from 21 populations of the native (Europe) and the invasive range (North-America) were grown under common greenhouse conditions. According to the EICA hypothesis it was predicted that plants from the invasive range might show stronger growth and have lower levels of defence as a result of selection favouring such genotypes. There was significant variation between populations in shoot, root, total biomass, and number of ramets of 3-month-old plants but no difference due to origin from both continents. The main glucosinolate p-hydroxybenzyl glucosinolate was significantly higher in seedlings of the invasive range while myrosinase activity was higher in old plants of the invasive range. Therefore, the EICA hypothesis does not hold, however, alternatively there is evidence for selection favouring stronger defence in the invasive range. The binary defence system of this crucifer is discussed with respect to the degree of specialisation of potential herbivores.