Very Long Baseline Interferometry is the only technique that can estimate Earth nutations with an accuracy under the milliarcsecond level. With 35 years of geodetic VLBI observations, the principal nu- tation terms caused by luni-solar tides and geophysical response have been estimated. We focus on the vari- ability. Two of them present very significant amplitude and phase variations: the retrograde Free Core Nuta- tion (FCN) with a period of around 430 days and the Annual Retrograde Nutation (ARN). Despite progress made in global circulation models, the atmospheric and ocean excitation cannot account for that. In particular the ARN shows an amplitude modulation of approxi- mately six years, reminiscent of the six-year geomag- netic oscillation in the Length-of-Day (LOD). As to the latter, we suggest that the nutation term variability may have deep Earth causes, and we estimate an order of magnitude of Earth internal structure parameters to ex- plain this variability. Keywords Nutation, least-squares adjustment, ARN 1 Introduction The last approved nutation model, MHB2000 [14], was derived from VLBI data. They have adjusted 1365 luni- solar and planetary terms, associating constant ampli- tudes and phases with each of them. But this model was unsuccessful in explaining the free core nutation (FCN) that increases by more than 100 μas at some SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universit ́ es, UPMC Univ. times. This nutation arises from a geophysical response to luni-solar attraction, and it finds its source in the cou- pling between the fluid outer core and the mantle. This coupling can be of viscous nature, of electromagnetic nature, or due to the topography of the boundary. Therefore, to estimate correctly the variation of the FCN is important for the understanding of the in- ner structure of the Earth. Many studies have been published on its estimation, and several models exist: Malkin (2013) [12], Kr ́ asn ́ a et al. (2013) [10], Belda et al. (2016) [1]. One of them has been selected as ref- erence by the IERS: the Lambert model 1 [16]). These works have in common that they estimate the variabil- ity using a window with a width on the order of the FCN period. The proximity of the annual retrograde nutation (ARN) with the FCN can be dangerous be- cause of the beat phenomenon. Given the variability of the FCN and possibly of the ARN, a least-squares ad- justment approach may not succeed.