Biological invasions are a major threat to biological diversity, agriculture, and human health. To predict and prevent new invasions, it is crucial to develop a better understanding of the drivers of the invasion process. The analysis of 4,533 border interception events revealed that at least 51 different alien ant species were intercepted at US ports over a period of 70 years (1914-1984), and 45 alien species were intercepted entering New Zealand over a period of 68 years (1955-2013). Most of the interceptions did not originate from species' native ranges but instead came from invaded areas. In the United States, 75.7% of the interceptions came from a country where the intercepted ant species had been previously introduced. In New Zealand, this value was even higher, at 87.8%. There was an overrepresentation of interceptions from nearby locations (Latin America for species intercepted in the United States and Oceania for species intercepted in New Zealand). The probability of a species' successful establishment in both the United States and New Zealand was positively related to the number of interceptions of the species in these countries. Moreover, species that have spread to more continents are also more likely to be intercepted and to make secondary introductions. This creates a positive feedback loop between the introduction and establishment stages of the invasion process, in which initial establishments promote secondary introductions. Overall, these results reveal that secondary introductions act as a critical driver of increasing global rates of invasions.