This paper deals with a vector control of n-phase permanent magnet synchronous machine. To use control algorithms already developed for sine-wave 3-phase machines, the spectrum of back electromotive force (EMF) must contain only odd 2k+1 harmonics which verify the following inequality, 1≤ 2k +1< n . In an experimental vector control of a 5-phase drive, two usual algorithms of sine-wave 3-phase machine are thus used to supply a machine with trapezoidal waveform back EMF. In this case, the first and third harmonics are used to produce torque: the other harmonics, and particularly the 7th one, induce effects as torque ripples and parasitic currents.