<p>Subduction invasion has been referred to as the process by which subduction zones from a subducting ocean invade or trigger subduction initiation in a contiguous ocean. This can, in principle, happen in different ways that can vary from a direct migration by rollback along an oceanic corridor connecting the two oceans (e.g., the Gibraltar Arc into the Atlantic) or by polarity reversal across a narrow continental land bridge, potentially involving the collision of an ocean plateau with the pre-existent trench (the Scotia and the Caribbean arcs). This process is important because new subduction zones are difficult to start in the present plate tectonics context and most known examples of initiation seem to be forced by pre-existent subduction zones. The problem is that in internal Atlantic-type oceans there are no pre-existent subduction zones, and therefore, they must be introduced from the outside. Luckily, the Atlantic seems to be just passing through a phase of invasion, as evidenced by the three referred examples. But while the Caribbean and the Scotia arcs are already two fully formed Atlantic-subduction systems, the Gibraltar Arc is currently in the process of migrating between oceanic basins. In the future, the Arc can evolve according to two different scenarios. In the first, the Gibraltar Arc is stuck between Africa and Iberia and the subduction is waning. In the other scenario, after a period of quiescence, the arc manages to go through and invade the Atlantic. In order to understand which is more feasible, we have developed 3D numerical models using the code LaMEM to gain some insights into how this system may evolve. We have simulated the development of the Mediterranean arc-back-arc system, with rollback and the retreat of the subduction zones in a fully dynamic framework (no active kinematic boundaries). Our model shows that under the studied parameters, the Gibraltar subduction zone manages to invade the Atlantic, even in the cases of a very narrow oceanic corridor. However, this led to a very significant decrease in the subduction velocity, suggesting that in the natural prototype, a period of quiescence is expected before the Mediterranean subduction zone manages to go through and invade the Atlantic.</p><p>J.C. Duarte and F.M. Rosas acknowledge financial support by FCT through the project UIDB/50019/2020 – Instituto Dom Luiz (IDL)</p>