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This paper provides a general theoretical description of a weakly bound atomic system (a negative ion) interacting simultaneously with two (generally strong) fields, a static electric field and a monochromatic laser field having an arbitrary elliptical polarization. The zero-range δ-potential is used to model the interaction of a bound electron in a negative ion as well as the interaction of a detached electron with the residual atom. Our treatment combines the quasistationary (complex energy) and quasienergy (Floquet) approaches. This quasistationary, quasienergy state (QQES) formalism is the most appropriate one for analysing a decaying quantum system under the influence of a periodic external perturbation. Existing QQES theory is reviewed and some new results are discussed: the Hellmann–Feynman theorem and the normalization procedure for QQES, and the definition of the dipole moment and the dynamic polarizability for a decaying atomic system (in strong static electric and/or laser fields). These results are illustrated using analytical formulae obtained from an exact solution of the QQES problem for a δ-model potential in two strong fields. Finally, from the imaginary part of the dynamic polarizability we obtain analytic results (to first order in the laser-field intensity) for the photodetachment cross section. Our results are then compared with those of previous theoretical studies.