The first evidence of the occurrence of nucleosynthesis in stars was provided in the 
1950s by the detection of the unstable heavy element technetium in the atmospheres 
of stars on the Asymptotic Giant Branch (AGB), a late evolutionary phase of stars of 
low mass. Technetium can be produced by slow neutron captures (the s process) and 
thus its detection requires that neutron source reactions are activated in these 
stars, triggering the production of heavy element.  The best candidates as sources 
of neutrons have been identified in the C13(alpha,n)O16 and
Ne22(alpha,n)Mg25 reactions. The C13(alpha,n)O16 reaction appears to be responsible 
for the production of most of the neutrons, while the
Ne22(alpha,n)Mg25 reaction is important for the activation of branching points on 
the s-process path. Detailed evidence of the operation of branching points is shown 
by recent measurements of the isotopic composition of heavy elements in meteoritic 
silicon carbide (SiC) grains that originated from AGB stars. Interesting examples 
that will be discussed are the Ba134/Ba136, Kr86/Kr82 and Zr96/Zr94 ratios. During 
the s process, elements lighter than iron represent "neutron poisons", stealing 
neutrons from the production of heavy elements. Nevertheless, neutron captures on 
light elements are of much interest in triggering secondary nucleosynthesis path. 
For example, the activation of the
N14(n,p)C14 reaction on one hand can strongly inhibit the production of heavy 
elements by the C13(alpha,n) source, on the other hand it leads to the production of 
fluorine, which is observed to be enhanced in AGB stars.
Neutron-capture reactions on the isotopes of Mg, Si and Ti are also of great 
interest as they change the composition of these elements, which are also recorded 
in meteoritic grains.