Résumé : The discoveries of two extremely iron-poor stars with [Fe/H]<-5, HE0107-5240 and HE1327-2326 provided the great opportunities of verifying whether these stars are the survivors of the first generation stars; the very weak lines of detected metals in their atmospheres can be extrinsic source that is the accretion from interstellar gas or from binary companion, rather than intrinsic one. In this work, we explore the possibility that these stars were born in binary systems from the primordial clouds by considering the results of stellar evolution and nucleosynthesis in metal-free models of low to intermediate mass AGB stars. Observed abundance patterns for these 2 stars are in agreement with the results and can be explained by the binary scenario that observed stars disguise their surface abundances by the mass transfer in the binary system. In particular, we first demonstrated the reproduction of Sr without large enhancement of Ba through the neutron capture reactions in the helium flash convective region of AGB models without any iron seeds for s-process. The apparent lack of stars in -5 < [Fe/H] < -4 may suggest the effect of dilution by the surface convection at the red giant branch. If this is true, other Pop.III survivors can be discovered at the main sequence having [Fe/H] ∼ -3, whose surface abundances are changed by the mass transfer from evolved companions in binary systems. © 2006 American Institute of Physics.