We generalize the description of the attractor mechanism based on an effective black hole potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to , as well. Thence, we work out the example of the model of supergravity in the presence of Fayet-Iliopoulos terms, for the supergravity analogues of the magnetic and black hole charge configurations, and in three different symplectic frames: the , covariant and -truncated ones. The attractive nature of the critical points, related to the semipositive definiteness of the Hessian matrix, is also studied.