The purpose of this paper is to present a general theory for describing a spin assembly under a nearly resonant rotating magnetic field of arbitrary strength. According to the relation between the static local field strength σ0 and the characteristic frequency φ0 of fluctuation of the environment two important cases are classified. A) If the fluctuation of the environment dominates (φ0 ≫ σ0), the equation becomes essentially stochastic in type and we can safely define relaxation times in Bloch's sense with a modification that the restoring force is proportional to the deviation not from the canonical distribution under the constant magnetic field but from the canonical distribution under the total magnetic field in an instantaneously static system of coordinates (i.e. the modified Bloch equation holds). B) If, on the other hand, the static local field dominates (σ0 ≫ φ0), then the transverse lifetime depends essentially on the strength of the rotating field, in fact it is prolonged upon saturation. The leads to a general and reasonable explanation of “saturational narrowing” and the anomalous saturational behaviour of dispersion mode such as have been observed by Redfield and others in the case of nuclear resonance in metals. The same kind of classification applies to the case in which we have two interacting different species of spin, and a general treatment will be given in a forthcoming paper.