  Numerical simulations of dwarf spheroidal galaxies undergoing several close
encounters with the Milky Way are described. By comparing our models to
observed properties of the recently discovered dwarf galaxy in Sagittarius
(Sgr), we discuss implications of our results for the formation and evolution
of the Milky Way system. We find that existing observations are not sufficient
to allow us to place precise limits on either the orbit or the initial state of
the dwarf. Debris from the ongoing tidal stripping of the Sagittarius galaxy
are expected to form moving groups in the halo of the Galaxy and the discovery
of such stars would strongly constrain the history and dynamical state of the
dwarf. Furthermore, if Sgr is presently being disrupted, we predict that its
remains will be detectable as a moving group in the halo for more than 1 Gyr.
Thus, if similar accretion events have occurred in the recent history of the
Galaxy, their aftereffects may still be observable.
