It is suggested that flow patterns without axial symmetry may occur when an axial-compressor stage operates in a steady, uniform stream, provided that the blade airfoil characteristics exhibit certain peculiarities. For example, blades acting close to the stall may show nonlinearity, hysteresis, and/or time lags, and these may cause asymmetric flow patterns. Conditions necessary for existence of such phenomena are analyzed by consideration of an annulus of infinitely many blades and very large radius. It is shown that rotational-flow effects due to vortex shedding by the blades must be considered. The induced velocities resulting from asymmetrical loadings are calculated. The final step of the calculation is to show that these induced effects may actually support the circulation distribution that produces them. This step is only partly taken in the present paper. It is shown that time lag in the development of lift of a blade may produce such “eigen-solutions.” Detailed study of the results of non-linearity in the blade characteristics is left for another investigation.