The present invention provides a circuit for monitoring harmonic distortion in the power supply of a synchronous electrical machine with permanent magnet excitation that comprises a rotor without a damper cage, a stator with first, second, and third windings, a frequency converter, and control circuits for controlling the frequency converter. The monitoring circuit comprises means for obtaining at least one signal representative of the current in the first winding of the stator and at least one signal representative of the current in the second winding of the stator; a circuit for generating synchronizing pulses reflecting the electrical frequency fn of rotation of the rotor relative to the stator; means for determining a signal representative of the current in the third winding of the stator; a set of band-stop notch filters respectively receiving said signals representative of the currents in the first, second, and third windings, and each presenting a center frequency that is servo-controlled to the electrical frequency fn of rotation of the rotor, in order to reject the harmonic corresponding to said electrical frequency fn; a set of measurement circuits for measuring the harmonics that remain in the signals output by each of the band-stop notch filters; and a comparator circuit for continuously comparing the greatest of the values of the signals from the measurement circuits relative to an alarm threshold.