The resonance due to the nearly diurnal free wobble, observed in the diurnal tesseral tides and in the associated nutations, is used to determine the frequency and the damping of this wobble. The data are stacked to provide a least squares estimation of the resonance parameters: frequency, quality factor, and complex strengths. Some previous papers presented the same kind of analysis using either tidal or nutation data sets; in both cases, the frequency was about -(1+1/435) cycle/sidereal day, but the quality factor was larger for nutation data than for tidal data. In this paper we analyze simultaneously both sets of data, and we focus our attention on the determination of the free core nutation period and quality factor. We have analyzed a series of tidal data sets provided by the International Center for Earth Tides (ICET), and nutation data sets gathered from published matter. Our final result is obtained from a global stacking using four independent nutation data sets and three superconducting gravimeter data sets together. The values of the fitted parameters are found to be λFCN=-(1+1/(434.1¿0.9)) cycle/sidereal day and Q≂54,000 (36,000; 109,000). ¿ American Geophysical Union 1994