  ESA's Global Astrometric Interferometer for Astrophysics (GAIA) holds the
promise of mapping out the detailed phase space structure of the Galactic halo
by providing unprecedented annual proper motion and parallax of $1-10\muas$
astrometric accuracy (Gilmore et al. 1998). Unlike NASA's Space Interferometry
Mission (SIM), which will achieve similar accuracies but is a pointed
instrument, GAIA will be able to construct a global catalogue of the halo. Here
we study proper motions of giant branch stars in a tidal debris torn from a
small satellite system in the halo. We follow the evolution of a cold stream on
a polar orbit between 8-50 kpc in a variety of histories of the Galactic
potential, and observe the bright ($V<18$mag) members of the debris tail with
GAIA accuracy. We simulate effects due to the growing or flipping of the
Galactic disk over the past 4 Gyrs or the perturbation from a massive accreted
lump such as the progenitor of the Magellanic Clouds. Our simulations suggest
that the results of Johnston, Zhao, Spergel & Hernquist (1999) and Helmi, Zhao
& de Zeeuw (1999) for static Galactic potentials are likely to be largely
generalizable to realistic time-dependent potentials: a tidal debris remains
cold in spite of evolution and non-axial symmetry of the potential. GAIA proper
motion measurements of debris stars might be used to probe both Galactic
structure and Galactic history. We also study several other factors influencing
our ability to identify streams, including accuracy of radial velocity and
parallax data from GAIA, and contamination from random field stars. We conclude
that nearby, cold streams could be detected with GAIA if these cousins of the
Sagittarius stream exist.
