The qualification and the maintenance of the International Celestial Refere
nce Frame (ICRF) source directions are currently based on global statistics
regarding the complete data set of VLBI observations of extragalactic radi
o sources. The founding hypothesis in the selection of extragalactic object
s to access a quasi-inertial reference system is that their directions are
fixed in space. Therefore the study of the time variability of the sources
is an important step in the process of checking and improving the reliabili
ty of the ICRF, in view of high precision applications such as Earth rotati
on studies or the unification with future space astrometry results. In this
paper we investigate the systematic and random behaviours in time series o
f individual determinations of coordinates for several hundred sources over
1987-1999. New criteria for the qualification of sources in a future revis
ion of the ICRF are proposed.