  The concept of overshoot has already been considered for numerous cases in
stellar evolution calculations. We explore the consequences of overshoot at the
convection zone which forms during the He-flash (thermal pulse) in AGB stars.
We find dramatic changes for the abundances within the intershell region as
well as for the mechanism of the 3rd dredge-up. That means that both the
predicted evolution of structural quantities as well as the chemical evolution
at the surface will be different, if overshoot is considered. We also present
evidence for the presence of overshoot during the He-flash from detailed model
calculations of the post-AGB phase and the comparison with observations. The
new evolutionary models show that a very late thermal pulse during the post-AGB
evolution can bring the intershell material up to the surface with minimal
modification due to convective H-burning. The good agreement of the surface
abundances of these models with observed surface abundances of H-deficient
post-AGB stars is interpreted as a strong support for the presence of overshoot
during the thermal pulses of AGB stars.
