We discuss in detail the evolutionary properties of low mass stars M< 1 M(Solar) having metallicity lower than Z=10^(-6) from the pre- main sequence up to (almost) the end of the Asymptotic Giant Branch phase. We also discuss the possibility that the large [C,N/Fe] observed on the surface of the most Iron poor star presently known, HE0107-5240, may be attributed to the autopollution induced by the penetration of the He convective shell into the H rich mantle during the He core flash of a low mass, very low metallicity star. On the basis of a quite detailed analysis, we conclude that the autopollution scenario cannot be responsible for the observed chemical composition of HE0107-5240.