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International audience; Neutron-induced cross sections of short-lived nuclei are highly relevant in many domains such as fundamental nuclear physics, astrophysics and applications in nuclear technology. In particular, these cross sections are essential for understanding the synthesis of elements via the s- and r stellar processes. However, the measurement of such cross sections with current techniques is very difficult or even impossible, because of the difficulties to produce and handle the necessary amounts of radioactive nuclei. Reaching the nuclei of interest is only possible by inverting the reaction kinematics with radioactive beams. In this contribution we present a project for indirectly determining neutron cross sections via the surrogate-reaction method. This project is based on the measurement of transfer- or inelastic-scattering-induced decay probabilities in inverse kinematics at storage rings. The measured probabilities are then used to tune nuclear-reaction models that will provide much more accurate predictions of the desired neutron cross sections. We also discuss a very ambitious, long-term project to directly measure neutron cross sections in inverse kinematics. It consists in the combination of a radioactive beam facility, an ion storage ring and a spallation neutron source.