Recent spectroscopic and morphological observational studies of galaxies ar
ound NGC 1399 in the Fornax Cluster have discovered several "ultracompact d
warf" galaxies with intrinsic sizes of similar to 100 pc and absolute B-ban
d magnitudes ranging from -13 to -11 mag. In order to elucidate the origin
of these enigmatic objects, we perform numerical simulations on the dynamic
al evolution of nucleated dwarf galaxies orbiting NGC 1399 and suffering fr
om its strong tidal gravitational field. Adopting a plausible scaling relat
ion for dwarf galaxies, we find that the outer stellar components of a nucl
eated 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. T
he nucleus, however, manages to survive. We also find that the size and lum
inosity of the remnant are similar to those observed for ultracompact dwarf
galaxies, if the simulated precursor nucleated dwarf has a mass of similar
to 10(8) M.. These results suggest that ultracompact dwarf galaxies could
have previously been more luminous dwarf spheroidal or elliptical galaxies
with rather compact nuclei.