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In this study, three empirical Free Core Nutation (FCN) models developed tothe present time, MHB2000, Malkin's and Lambert's ones, are compared on thebasis of representation of variations of the FCN amplitude and phase predictedby these models. It is possible to conclude, that the model of the authorprovides the most realistic representation of the FCN variations. However, thespecified models are based on representation about single FCN rotational mode.At the same time, some results of processing of the VLBI observations madeduring last years, specify possible presence of two close FCN periods. Atheoretical explanation to presence of a second FCN frequency FCN has beengiven by G. Krasinsky in his theory of rotation of the Earth with two-layerliquid core, ERA2005. In the present work, for more detailed studying thisphenomenon, the IVS time series of celestial pole offset, and also thosepredicted by the ERA2005 theory, have been investigated by means of severalstatistical methods which confidently show presence of two fluctuations innutational movement of an Earth's rotation axis with the periods about -452 and-410 solar days.

An analysis of celestial pole offset observations in the free core nutation frequency band