  We study the nucleosynthesis of several neutron capture elements (barium,
europium, lanthanum, and yttrium) in local group dwarf spheroidal (dSph)
galaxies and in the Milky Way by comparing the evolution of [Ba/Fe], [Eu/Fe],
[La/Fe], [Y/Fe], [Ba/Y], [Ba/Eu], [Y/Eu], and [La/Eu] observed in dSph galaxies
and in our Galaxy with predictions of detailed chemical evolution models. The
models for all dSph galaxies and for the Milky Way are able to reproduce
several observational features of these galaxies, such as a series of abundance
ratios and the stellar metallicities distributions. The Milky Way model adopts
the two-infall scenario, whereas the most important features of the models for
the dSph galaxies are the low star-formation rate and the occurrence of intense
galactic winds. We predict that the [s-r/Fe] ratios in dSphs are generally
different than the corresponding ratios in the Milky Way, at the same [Fe/H]
values. This is interpreted as a consequence of the time-delay model coupled
with different star formation histories. In particular, the star-formation is
less efficient in dSphs than in our Galaxy and it is influenced by strong
galactic winds. Our predictions are in very good agreement with the available
observational data. The time-delay model for the galactic chemical enrichment
coupled with different histories of star formation in different galaxies allow
us to succesfully interpret the observed differences in the abundance ratios of
s- and r- process elements, as well as of $\alpha$-elements in dSphs and in the
Milky Way. These differences strongly suggest that the main stellar populations
of these galaxies could not have had a common origin and, consequently, that
the progenitors of local dSphs might not be the same objects as the building
blocks of our Galaxy.
