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This paper presents an extension of a recently developed three-dimensional inverse method for turbomachine blades to handle multi-stage machines in the limit of an infinite number of blades in each blade row. The axisymmetric flowfield is assumed to be inviscid, compressible, and rotational. The use of blockage and entropy-increase terms are included in the theory to model losses. An iterative procedure is presented for the calculations of the blade profiles which produce prescribed swirl schedules in the bladed regions. The numerical technique employed to solve the relevant equations is based on a finite-volume formulation. The method is applied to the design of a low-pressure multi-stage centrifugal compressor used in industrial processing.