The possibility of creating population inversions in multiline Mo¨ssbauer nuclei by a two‐stage process, employing neutron capture to generate resonance radiation that then excites states in a separate region, is investigated. Geometrical and kinetic factors and dependences of the interstage coupling on isomer ratios and Mo¨ssbauer parameters are determined. Rate equations for one hypothetical and four actual Mo¨ssbauer isotopes are solved in an approximation that overestimates the excitation; nevertheless, it is found that the necessary neutron capture rates are thermodynamically unattainable.