New series of rigid and non-rigid Earth nutation. Comparison with observations J. Souchay After analysing the recent developments of the theory of the nutation for a simplified rigid Earth model (Kinoshita and Souchay, 1990) with new corrections and new contributions (Souchay and Kinoshita,1995), we will study the effect of these developments on the calculation of the coefficients of nutation for a non-rigid Earth model, based on the transfer function given by Wahr(1979). The relative improvements characterized by the residuals with the observations will be discussed.