Evolution and surface abundances of red giants experiencing deep mixing

We have calculated the evolution of low metallicity red giant stars under t he assumption of deep mixing between the convective envelope and the hydrog en burning shell. We find that the extent of the observed abundance anomali es, and in particular the universal O-Na anticorrelation, can be totally ex plained by mixing which does not lead to significant helium enrichment of t he envelope. On the other hand, models with extremely deep mixing and stron g helium enrichment predict anomalies of sodium and oxygen, which are much larger than the observed ones. This latter result depends solely on the nuc leosynthesis inside the hydrogen burning shell, but not on the details of t he mixing descriptions. These, however, influence the evolution of surface abundances with brightness, which we compare with the limited observational material available. Our models allow, nevertheless, to infer details on th e depth and speed of the mixing process in several clusters. Models with st rong helium enrichment evolve to high luminosities and show an increased ma ss loss. However, under peculiar assumptions, red giants reach very high lu minosities even without extreme helium mixing. Due to the consequently incr eased mass loss, such models could be candidates fur blue horizontal branch stars, and, at the same time, would be consistent with the observed abunda nce anomalies.