  Aims: The effect of frequency-dependent AGN core positions (``core-shifts'')
on radio Very Long Baseline Interferometry (VLBI) global astrometry
measurements is investigated.
  Methods: The basic equations relating to VLBI astrometry are reviewed,
including the effects of source structure. A power-law representation of
core-shifts, based on both observations and theoretical considerations of jet
conditions, is incorporated.
  Results: It is shown that, in the presence of core-shifts, phase and
group-delay astrometry measurements yield different positions. For a core
displacement from the jet base parametrized by Delta x (lambda) = k lambda^beta
group delays measure a ``reduced'' core-shift of (1-beta) Delta x (lambda). For
the astrophysically-significant case of beta = 1, group delays measure no shift
at all, giving the position of the jet base. At 8.4 GHz an estimated typical
offset between phase and group-delay positions of ~170 uas is smaller than the
current ~250 uas precision of group-delay positions of the sources used to
define the ICRF; however, this effect must be taken into account for future
measurements planned with improved accuracy when comparing with optical
positions of AGN to be obtained with the GAIA mission.
