We have computed and analyzed the evolution of intermediate-mass stars of metallicity Z = 10−5 from the main sequence until the early stages of the TP-(S)AGB phase. In order to check the influence of mixing we have performed our calculations using two different evolutionary codes, EVOLVE — which does not include diffusion but allows for overshooting— and LPCODE, which includes diffusion and overshooting “à-la-Herwig”. Important differences appear during the TP– AGB phase, as the calculations done with EVOLVE lead to an almost negligible third dredge-up, whereas the sequences computed with LPCODE show important third dredge-up and, therefore, significant enrichment in metals of the envelope. This fact has consequences on the strength of the winds during the TP-AGB phase and, ultimately, on the final fate of the considered stars. Also, the models computed with LPCODE show strong double flashes produced by the ingestion of protons on the helium burning shell.