It is known that the torque density of multiphase motors can be increased by superimposing high-order spatial harmonics to the fundamental one in the air-gap magnetic field. However, the problem of maximizing the torque capability is still controversial, since the results depend on the constraints that have been considered. The analysis presented in this paper shows how to maximize the magnetic torque under the same rms value of the stator current. Finally, two control schemes for high torque-density multiphase induction motors are illustrated. Some experimental tests confirm the validity of the theoretical analysis.