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A VLBI series of celestial pole offsets has been used for deriving the corrections to the main terms of the IAU 1980 nutation series using the least squares solution and amplitude spectra method. The results are compared with current geophysical models. The discrepancies between observations and theory are largely due to deficiencies in the nutation models. A retrograde periodic variation (at a period of 420.0 days) has been revealed. The free mode will give us futher information on the core-mantle boundary.doi:10.1017/s0074180900173541 fatcat:s3zwuladsrdkpbb24a4lbodh6m