The relationship between the Bloembergen-Purcell-Pound theory of resonance saturation and the Redfield theory is discussed in terms of the effect of a weak perturbation acting for a long time on a spin system perfectly isolated from the lattice. A simple derivation of Provotorov's rate equations is given, based on Schumacher's concepts. The theoretical ideas are applied to the F19 resonance in CaF2 to discuss the phenomenon of rotary saturation, in which one applies a radio-frequency field H1, and modulates the static field at a frequency a such that H1a, where is the nuclear gyromagnetic ratio. When H1 is large compared to the local field, the rotary saturation is described by Redfield's concepts; when H1 is comparable to the local field, the original Bloembergen-Purcell-Pound theory works. © 1966 The American Physical Society.