We have computed the evolution of Super-AGB stars from the main sequence and up to a few hundred thermal pulses, with special attention to the low metallicity cases (Z = 10􀀀10; 10􀀀5; 10􀀀4 and 10􀀀3). Our computations have been performed using time– dependent mixing and new opacity tables that admit variations in the abundances of carbon and oxygen. By following the evolution along the main central burning stages and the early TP-SAGB, we resolve the upper mass limits for the formation of TP-SAGB stars and determine the mass range at which the dredge-out phenomenon occurs. This phenomenon involves the merger of a convective shell sustained by helium burning at the top of the degenerate core with the hydrogen–rich convective envelope and the occurrence of a hydrogen flash. The dredge–out allows elements synthesised through helium burning to be transported to the stellar surfaces and therefore it can a ect the initial composition of the TP-SAGB stars.