In our study we find, from the analysis of VLBI observations, small quasi-periodic fluctuations of the period and quality factor of retrograde Free Core Nutation (FCN), ranging mainly between 429.8 to 430.8 days and 17000 to 21000, respectively. To this end, we use resonant effects in several dominant forced nutation terms to calculate the period and quality factor of FCN in running 6-year intervals. We also recently demonstrated that the atmospheric and oceanic excitations are capable of exciting FCN. Both amplitude and phase of the geophysically excited motion are consistent with the values observed by VLBI, in the interval of tens of years. The geophysical excitations are now numerically integrated, using Brzeziński’s broadband Liouville equations, and removed from the observed celestial pole offsets. The remaining part is then used to derive the period and quality factor of FCN in running intervals, and to study the temporal stability of these important Earth parameters. It is demonstrated that the observed quasi-periodic variations of both parameters are probably not caused by these geophysical excitations., Jan Vondrák and Cyril Ron., and Obsahuje bibliografii