Previous case studies have illustrated the strong local influence of tropical cyclones (TCs) on CO2 air-sea flux suggesting that they can significantly contribute to the global In this study, we use a state-of-the art global ocean biochemical model driven by TCs wind forcing derived from a historical TCs database, allowing to sample the response under 1663 TCs. Our results evidence a very weak contribution of TCs to global one or two order of magnitude smaller than previous estimates extrapolated from case studies. This result arises from several competing effects involved in the response to TCs, not accounted for in previous studies. While previous estimates have hypothesized the ocean to be systematically oversaturated in CO2 under TCs, our results reveal that a similar proportion of TCs occur over oversaturated regions (i.e. the North Atlantic, Northeast Pacific and the Arabian Sea) and undersaturated regions (i.e. Westernmost North Pacific, South Indian and Pacific Ocean). Consequently, by increasing the gas exchange coefficient, TCs can generate either instantaneous CO2 flux directed from the ocean to the atmosphere (efflux) or the opposite (influx), depending on the CO2 conditions at the time of the TC passage. A large portion of TCs also occurs over regions where the ocean and the atmosphere are in near equilibrium, resulting in very weak instantaneous fluxes. Previous estimates also did not account for any asynchronous effect of TCs on during several weeks after the storm, oceanic pCO2 is reduced in response to vertical mixing, which systematically causes an influx anomaly. This implies that, contrary to previous estimates, TCs weakly affect the CO2 efflux when they blow over supersaturated areas because the instantaneous storm wind effect and post-storm mixing effect oppose with each other. In contrast, TCs increase the CO2 influx in undersaturated conditions because the two effects add up. These compensating effects result in a very weak contribution to global and a very modest contribution to regional interannual variations (up to 10%).