Two alternative scenarios concerning the origin and evolution of extremely metal-poor halo stars are investigated. The first one assumes that the stars have been completely metal-free initially and produced observed carbon and nitrogen overabundances during the peculiar core helium flash typical for low-mass Population-III stars. The second scenario assumes that the initial composition resulted from a mixture of primordial material with ejecta from a single primordial supernovae. Both scenarios are shown to have problems in reproducing C, N, and O abundances simultaneously, and both disagree with observed 12C/13C-ratios,though in different directions. We concentrate on the most iron-poor, carbon-rich object of this class, HE0107-5240, and conclude that the second scenario presently offers the more promising approach to understand these objects, in particular because evolutionary tracks match observations very well.
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