Based on evolutionary computations of 90 stellar models, we have analysed the impact of initial composition and core overshooting on the post-He-burning evolution and the associated nucleosynthesis of Super-AGB stars, pointing particular attention on
the C-burning phase. Moreover the possible link between the transition masses $M_{up}$, $M_{N}$ and $M_{mas}$ (defined as the critical initial mass above which C-burning ignites, the minimum initial mass for an electron-capture supernova and the minimum initial mass for the completion of all the nuclear burning phases respectively) and the properties of the core during the core He-burning phase is also briefly discussed.
