  The dwarf galaxies of the Local Group can be separated in three morphological
groups: irregular, elliptical and spheroidal. As in the large galaxy clusters,
there seems to be a morphology-position relationship: irregular galaxies are
preferentially found in the outskirts (low density regions) of the Local Group,
whereas dwarf ellipticals and spheroidals are more frequent in the central,
high density regions. To cast light on the nature and origin of dwarf galaxies
in the Local Group, Mayer et al.(2001) have suggested that a dwarf irregular
galaxy tidally interacting with a galaxy of much larger mass may be re-shaped
into a dwarf spheroidal or elliptical object. In this paper we check by means
of N-Body Tree-SPH simulations whether this is possible for a selected sample
of galaxies of the Local Group. Using the best data available in literature to
fix the dynamical and kinematical status of a few dwarf galaxies in the Local
Group, we follow the evolution of an ideal satellite, which supposedly started
as an irregular object during its orbital motion around the Milky Way. We find
that the tidal interactions with the Milky Way remove a large fraction of the
mass of the dwarf irregular and gradually reshape it into a spherical object.
