Abstract: A practical method,the spectral method,is developed to find the periodic solution of non linear ordinary differentical equations directly.By expanding the solution into its Fourier series with the frequency and the amplitudes of each harmonics to be determined,the problem of sloving the non linear ordinary differential equations is transformed into the solution of corresponding non linear algebraic equations.Two examples,the van der Plo equation and the mean field equations of the neuronal groups,are also presented to explain and discuss this algorithm.

Key words: Limit Cycle, Spectral Method