In this paper the program of establishment of the fundamental geodetic frame, covering the European and Asian part of Russian territory, is briefly described. This reference network, based on the main use of GNSS measurements, after its completion, could be an important contribution to the upgrading of the International Terrestrial Reference Frame and to the GGOS project. The precise data, obtained at the permanent sites, will provide more information for monitoring and studies of the tectonic movements in Eurasia. The results of first experiment on the use of full constellation of the GLONASS system for the precise positioning are considered. To compare the positioning accuracy estimated by the use of GLONASS and GPS, measurements obtained at 15 new sites of the Russian fundamental geodetic network were analyzed. Outcome of the performed computations shows that new sites of the Russian geodetic network were determined with the precision (rms) 3-10mm in spite of short period of measurements. The differences between coordinates of these new sites, estimated by only GPS or GLONASS measurements, are in the same limits. Nevertheless, for the achievement of the 1mm accuracy in site positioning, according to the demands of GGOS project, models used for data processing of the GLONASS system should be more carefully studied and compared.