  By means of a detailed chemical evolution model, we follow the evolution of
barium and europium in four Local Group Dwarf Spheroidal Galaxies, in order to
set constraints on the nucleosynthesis of these elements and on the evolution
of this type of galaxies compared with the Milky Way. The model, which is able
to reproduce several observed abundance ratios and the present day total mass
and gas mass content of these galaxies, adopts up to date nucleosynthesis and
takes into account the role played by supernovae of different types (II, Ia)
allowing us to follow in detail the evolution of several chemical elements (H,
D, He, C, N, O, Mg, Si, S, Ca, Fe, Ba and Eu). By assuming that barium is a
neutron capture element produced in low mass AGB stars by s-process but also in
massive stars (in the mass range 10 - 30 $M_{\odot}$) by r-process, during the
explosive event of supernovae of type II, and that europium is a pure r-process
element synthesized in massive stars also in the range of masses 10 - 30
$M_{\odot}$, we are able to reproduce the observed [Ba/Fe] and [Eu/Fe] as
functions of [Fe/H] in all four galaxies studied. We confirm also the important
role played by the very low star formation efficiencies ($\nu$ = 0.005 - 0.5
Gyr$^{-1}$) and by the intense galactic winds (6-13 times the star formation
rate) in the evolution of these galaxies. These low star formation efficiencies
(compared to the one for the Milky Way disc) adopted for the Dwarf Spheroidal
Galaxies are the main reason for the differences between the trends of [Ba/Fe]
and [Eu/Fe] predicted and observed in these galaxies and in the metal-poor
stars of our Galaxy. Finally, we provide predictions for Sagittarius galaxy for
which data of only two stars are available.
