The phenomenon known as ‘rotating stall’ is described. Basically, it involves a nonuniform pattern of flow, steadily rotating relative to both the fixed and the rotating blades of axial-flow compressors. Attempts to analyze the phenomenon by means of small-perturbation theories are reviewed. It is shown that the work of several investigators can be included in a single formulation and that they differ only in the type of blade-characteristic relations assumed. The present author's analyses based on linearized ‘airfoil’ and ‘channel’ relations are presented in detail. The various theories coincide in the qualitative conclusion that self-induced rotating-stall patterns can occur in stalled, rigid blade rows. A comparison with available experimental results is inconclusive, so far as a choice between the several theories is concerned.