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We reanalyze the problem of Li abundances in red giants of nearly solarmetallicity. After an outline of the problems affecting our knowledge of the Licontent in low-mass stars (M<3Mo), we discuss deep-mixing models for the RGBstages suitable to account for the observed trends and for the correlatedvariations of the carbon isotope ratio; we find that Li destruction in thesephases is limited to masses below about 2.3 Mo. Subsequently, we concentrate onthe final stages of evolution for both O-rich and C-rich AGB stars. Here, theconstraints on extra-mixing phenomena previously derived from heavier nuclei(from C to Al), coupled to recent updates in stellar structure models(including both the input physics and the set of reaction rates used), aresuitable to account for the observations of Li abundances below A(Li)= loge(Li) = 1.5 (and sometimes more). Also their relations with othernucleosynthesis signatures of AGB phases (like the abundance of F, the C/O and12C/13C ratios) can be explained. This requires generally moderate efficiencies(\dot M <= 0.3 - 0.5 x 10^-6 Mo/yr) for non-convective mass transport. At suchrates, slow extra-mixing does not modify remarkably Li abundances in early-AGBphases; on the other hand, faster mixing encounters a physical limit indestroying Li, set by the mixing velocity. Beyond this limit, Li starts to beproduced; therefore its destruction on the AGB is modest. Li is thensignificantly produced by the third dredge up. We also show that effectivecirculation episodes, while not destroying Li, would easily bring the 12C/13Cratios to equilibrium, contrary to the evidence in most AGB stars, and wouldburn F beyond the limits shown by C(N) giants. Hence, we do not confirm thecommon idea that efficient extra-mixing drastically reduces the Li content ofC-stars with respect to K-M giants.

Deep Mixing in Evolved Stars. II. Interpreting Li Abundances in RGB and AGB Stars