An iterative unfolding method has been applied to several types of neutron environment to obtain neutron-flux spectra. The mathematical procedure involves selection of an initial spectral approximation and its subsequent perturbation to obtain a best-fit simultaneous solution for a system of ten or more activation integral equations. The present analytical studies support earlier results that integral neutron flux may be obtained from foil data with accuracies to within ± 10 to 30% at any point over the energy range from 4 × 10−7 to 18 MeV, if the activation cross-section data and measured activation rates are accurate to ± 10%.