Globalisation has facilitated the spread of alien species, and some of them have significant impacts on biodiversity and human societies. It is commonly thought that biological invasions have accelerated continuously over the last centuries, following increasing global trade. However, the world experienced two distinct waves of globalisation (~1820-1914, 1960-present), and it remains unclear whether these two waves have influenced invasion dynamics of many species. To test this, we built a statistical model that accounted for temporal variations in sampling effort. We found that insect and plant invasion rates did not continuously increase over the past centuries but greatly fluctuated following the two globalisation waves. Our findings challenge the idea of a continuous acceleration of alien species introductions and highlight the association between temporal variations in trade openness and biological invasion dynamics. More generally, this emphasises the urgency of better understanding the subtleties of socio-economic drivers to improve predictions of future invasions.