  We predict the metallicity distribution of stars and the age-metallicity
relation for 6 Dwarf Spheroidal (dSph) galaxies of the Local Group by means of
a chemical evolution model which is able to reproduce several observed
abundance ratios and the present day total mass and gas content of these
galaxies. The model 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, and Fe). Each galaxy model is specified by the prescriptions of the
star formation rate and by the galactic wind efficiency chosen to reproduce the
main features of these galaxies. These quantities are constrained by the star
formation histories of the galaxies as inferred by the observed color-magnitude
diagrams (CMD). The main conclusions are: i) 5 of the 6 dSphs galaxies are
characterized by very low star formation efficiencies ($\nu = 0.005 - 0.5 Gyr
^{-1}$) with only Sagittarius having a higher one ($\nu = 1.0 - 5.0 Gyr
^{-1}$); ii) the wind efficiency is high for all galaxies, in the range $w_i$ =
6 - 15; iii) a high wind efficiency is required in order to reproduce the
abundance ratios and the present day gas mass of the galaxies; iv) the
predicted age-metallicity relation implies that the stars of the dSphs reach
solar metallicities in a time-scale of the order of 2 - 6 Gyr; v) the
metallicity distributions of stars in dSphs exhibit a peak around [Fe/H] $\sim$
-1.8 to -1.5 dex, with the exception of Sagittarius ([Fe/H] $\sim$ -0.8 dex);
iv) the predicted metallicity distributions of stars suggest that the majority
of stars in dSphs are formed in a range of metallicity in agreement with the
one of the observed stars.
