  We present the results of s-process nucleosynthesis calculations for AGB
stars of different metallicities and initial masses. The computations were
based on previously published stellar evolutionary models that account for the
III dredge up phenomenon occurring late on the AGB. Neutron production is
driven by the 13C(alpha,n)16O reaction during the interpulse periods in a tiny
layer in radiative equilibrium at the top of the He- and C-rich shell. The
s-enriched material is subsequently mixed with the envelope by the III dredge
up, and the envelope composition is computed after each thermal pulse. We
follow the changes in the photospheric abundance of the Ba-peak elements (heavy
s, or `hs') and that of the Zr-peak ones (light s, or `ls'), whose logarithmic
ratio [hs/ls] has often been adopted as an indicator of the s-process
efficiency. The theoretical predictions are compared with published abundances
of s elements for Galactic AGB giants of classes MS, S, SC, post-AGB
supergiants, and for various classes of binary stars. The observations in
general confirm the complex dependence of n captures on metallicity. They
suggest that a moderate spread exists in the abundance of 13C that is burnt in
different stars. Although additional observations are needed, a good
understanding has been achieved of s-process operation in AGB. The detailed
abundance distribution including the light elements (CNO) of a few s-enriched
stars at different metallicity are examined.
