Two methods are presented for the computation of the time development of z magnetizations in multispin systems during and following application of irradiation at the resonance frequency of one of the spins. Method A includes explicit consideration of Uie response of the irradiated nucleus to the irradiating field, and can be used in cases where the irradiating power is low (γH2 ⪕ 1/T1). Method B assumes instantaneous saturation, and is appropriate when high irradiating power is used. In both cases the spin systems are assumed to consist of nuclei with distinct chemical shifts and negligible coupling constants. Sample calculations were performed on model proton systems, assuming long correlation times, typical of larger proteins or other biomacromolecules. These demonstrate that the time dependence of the nuclear Overhauser effect can be used in such systems to investigate relative internuclear distances and to probe for gaps separating islands or chains of nuclei. The use of high irradiating power is shown to be desirable. © 1979, American Chemical Society. All rights reserved.