Method for controlling an asynchronous electric machine of a power train of an electric or hybrid traction motor vehicle, comprising the following steps: a request for torque (C e #) and the mechanical rotational speed (Ω) of the asynchronous electric machine are determined, a request for rotor flux (φ r #) is determined as a function of a mapping dependent on the request for torque (C e #) and on the rotational speed (Ω), a request for the quadrature component of the stator current (I qs #) is determined as a function of the request for rotor flux (φ r #) and of the request for torque (C e #), a request for the direct component of the stator current (I ds #) is determined as a function of the request for rotor flux (φ r #), the angle that the rotating field (Θ s) forms with respect to a reference frame that is fixed with respect to the stator is determined as a function of the request for rotor flux (φ r #), of the request for the quadrature component of the stator current (I qs #), of the rotor angular frequency (ω r), of the number (p) of pairs of poles of the electric machine and of the mechanical rotational speed (Ω), the quadratic component (V qs) of the stator voltage is determined as a function of a combination of requests for the quadratic (I qs #) and direct (I ds #) components of the stator current, the direct component (V ds) of the stator voltage is determined as a function of another combination of requests for the direct (I ds #) and quadratic (I qs #) components of the stator current, the stator voltage values in the three-phase reference frame are determined as a function of the direct (V ds) and quadrature (V qs) components of the stator voltages in the Park reference frame and of the angle (Θ s) that the rotating field forms with respect to the reference frame that is fixed with respect to the stator, the three-phase stator voltage values thus determined are transmitted to the control means of the power supply inverter of the electric machine. a request for torque (C e #) and the mechanical rotational speed (Ω) of the asynchronous electric machine are determined, a request for rotor flux (φ r #) is determined as a function of a mapping dependent on the request for torque (C e #) and on the rotational speed (Ω), a request for the quadrature component of the stator current (I qs #) is determined as a function of the request for rotor flux (φ r #) and of the request for torque (C e #), a request for the direct component of the stator current (I ds #) is determined as a function of the request for rotor flux (φ r #), the angle that the rotating field (Θ s) forms with respect to a reference frame that is fixed with respect to the stator is determined as a function of the request for rotor flux (φ r #), of the request for the quadrature component of the stator current (I qs #), of the rotor angular frequency (ω r), of the number (p) of pairs of poles of the electric machine and of the mechanical rotational speed (Ω), the quadratic component (V qs) of the stator voltage is determined as a function of a combination of requests for the quadratic (I qs #) and direct (I ds #) components of the stator current, the direct component (V ds) of the stator voltage is determined as a function of another combination of requests for the direct (I ds #) and quadratic (I qs #) components of the stator current, the stator voltage values in the three-phase reference frame are determined as a function of the direct (V ds) and quadrature (V qs) components of the stator voltages in the Park reference frame and of the angle (Θ s) that the rotating field forms with respect to the reference frame that is fixed with respect to the stator, the three-phase stator voltage values thus determined are transmitted to the control means of the power supply inverter of the electric machine.