As the oceanic lithosphere ages and cools, its density increases and at some stage exceeds the density of the underlying asthenosphere, so that the plate can sink spontaneously under its own weight. However, despite the fact that some seafloors are ∼170 m.y. old, an undeniable Cenozoic example of a passive continental margin transforming into an active margin by subduction initiation is not yet known. Several workers have indicated the sources of difficulty of such a transformation; however, no evaluations of existing passive margins from the viewpoint of their future stability have been provided. As suggested by recent numerical experiments with generalized passive margin structures, spontaneous subduction initiation may have a hidden initial phase that is not expressed in diagnostic features such as trench and magmatic arc. Here we analyze numerically the probability of subduction initiation along the Atlantic American passive margins based on their topography and lithospheric and crustal structure. According to our experimental results, proper subduction will likely start during the next 10–20 m.y. along the southern part of the Brazilian margin, while other Atlantic margins of North and South America are stable under the present geodynamic conditions.