  Recent spectroscopic and morphological observational studies of galaxies
around NGC 1399 in the Fornax Cluster (Drinkwater et al. 2000b) have discovered
several `ultra-compact dwarf' galaxies with intrinsic sizes of $\sim$ 100 pc
and absolute $B$ band magnitudes ranging from -13 to -11 mag. In order to
elucidate the origin of these enigmatic objects, we perform numerical
simulations on the dynamical evolution of nucleated dwarf galaxies orbiting NGC
1399 and suffering from its strong tidal gravitational field. Adopting a
plausible scaling relation for dwarf galaxies, we find that the outer stellar
components of a nucleated dwarf are totally removed. This is due to them being
tidally stripped over the course of several passages past the central region of
NGC 1399. The nucleus, however, manages to survive. We also find that the size
and luminosity of the remnant are similar to those observed for ultra-compact
dwarf galaxies, if the simulated precursor nucleated dwarf has a mass of $\sim$
$10^8$ $M_{\odot}$. These results suggest that ultra-compact dwarf galaxies
could have previously been more luminous dwarf spheroidal or elliptical
galaxies with rather compact nuclei.
