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The maximum-power limits for high-speed permanent-magnet (PM) electrical machines for air compressor applications are determined in the speed range 20000-100000 r/min. For this purpose, five PM machines are designed and the electromagnetic, thermal, and mechanical designs of each machine are simultaneously performed. The critical values of the thermal and mechanical constraints are considered in order to obtain the maximum powers of the electrical machines. The electromagnetic losses generated in the machine are the output parameters of the electromagnetic design and input parameters for the thermal design. The thermal design is performed using a multiphysics method, which couples computational-fluid-dynamics equations with heat-transfer equations. The mechanical design considers the retention of the rotor elements against the huge centrifugal forces that arise during the high-speed operation and also the rotor dynamics properties of the rotor. The reliability of these design techniques is experimentally validated in the paper. The obtained maximum-power limit defines the speed-power region, in which the high-speed PM electrical machines intended for compressor applications can have a safe operation.