Résumé : Nuclear reactions induced by neutrons lead to the delayed emission of γ rays contributing to the instrumental background in γ-ray astrophysics missions in space. The cross sections for the reactions 27Al(n,2p)26Na, 27Al(n,α)24Na, and 56Fe(n,p)56Mn were measured up to a neutron energy of 50 or 65 MeV. A simple model was developed that allows one to extrapolate cross sections to higher energies. The magnitude of the instrumental background lines induced in the detectors of ESA's future INTEGRAL mission is deduced from our measurements.