  The third dredge-up phenomenon in asymptotic giant branch (AGB) stars is
analyzed through evolutionary model calculations of a \mass{3}, solar
metallicity star. The Schwarzschild criterion is used to test the stability of
a given layer against convection, and the calculations are performed either
with or without extra-mixing below the convective envelope. Based on these
calculations, several questions are addressed regarding the occurrence of the
third dredge-up in AGB star models, the laws governing that phenomenon, and
some of its implications on the structural and chemical evolution of those
stars.
