Doubly fed asynchronous machines have an outstanding property: they can be operated up to twice rated speed delivering full rated torque. This paper presents, for the first time in the literature, a control system for multiphase asynchronous machines fed by Voltage Source Inverters (VSIs) both in stator and rotor that incorporates the harmonic torques. The system has three main and distinctive features: the independent control of the fundamental and harmonic torques, a very fast dynamic response for each one of these torques and a powerful method for selecting the best suited inverter state to achieve the evolution of the fundamental and harmonics flux linkage space phasors prescribed by the external control loops. The first feature is achieved through the decoupling of the multiphase machine provided by the Space Phasor Theory (SPhTh). The second one comes from the application of the General Approach for a very Fast TOrque Control (GAFTOC) principle. The third feature relies on using for multi-phase VSIs a simple but powerful switching-table based mode of operation that overcomes the limitations of the switching-table based modes of operation developed up to now, that only enable for the inverter to feed machines with no harmonic torques contribution.