  In this study, three empirical Free Core Nutation (FCN) models developed to
the present time, MHB2000, Malkin's and Lambert's ones, are compared on the
basis of representation of variations of the FCN amplitude and phase predicted
by these models. It is possible to conclude, that the model of the author
provides the most realistic representation of the FCN variations. However, the
specified models are based on representation about single FCN rotational mode.
At the same time, some results of processing of the VLBI observations made
during last years, specify possible presence of two close FCN periods. A
theoretical explanation to presence of a second FCN frequency FCN has been
given by G. Krasinsky in his theory of rotation of the Earth with two-layer
liquid core, ERA2005. In the present work, for more detailed studying this
phenomenon, the IVS time series of celestial pole offset, and also those
predicted by the ERA2005 theory, have been investigated by means of several
statistical methods which confidently show presence of two fluctuations in
nutational movement of an Earth's rotation axis with the periods about -452 and
-410 solar days.
