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It is done an introduction into the problems of international celestial reference system (ICRS-I,II) realization. The expected and apparent motions of the remote radio sources are discussed. It is present the analysis of the ICRF-II catalog data: a) confirmation of the estimation of acceleration of the Solar system with respect to remote radio sources; b) detection of E-mode of apparent motion which could distinguish several option of Dark Energy: quintessence, Lambda term, or phantom Dark Energy.