We present a short overview of the activity of the IERS as well as the Main Astronomical Observatory (MAO) of the National Academy of Sciences of Ukraine for maintenance and extention of the International Celestial Reference Frame (ICRF). Special attention is given to the time stabilities of positions of radio sources (RS) and to the selection of a subset of RS to be used for maintenance of the ICRF. It is shown that seven RS qualified by the IERS as defining sources are unstable.