An approximate theory of the general perfect fluid flow in axial turbomachines is presented. The validity of the simplifying assumptions of the theory is justified by comparison with flow patterns measured in a large, low-speed, axial-flow compressor. It is concluded that the theory is convenient to apply and is sufficiently accurate for most engineering purposes. Performance data on blading designed for two and three-dimensional flow show that the blade types have comparable efficiencies. It is suggested that the advantages of unconventional blade types be exploited by designers. The flow regions in which fluid viscosity is important are shown. Experimental studies of cascade losses in the compressor indicate these losses to be greater than those measured in a cascade test tunnel. Measurements show that the rate of growth of the wall boundary layer need not be unusually great in an axial-flow compressor.