An important progress in the studies of metal-poor stars in the Galaxy
in the past decade is the discoveries of two stars having iron
abundances lower than the Sun by more than 100,000 times (hyper
metal-poor [HMP] stars). One of them was found and studied in detail
with the Subaru/High Dispersion Spectrograph (HDS). The chemical
compositions of these stars are believed to reflect the
nucleosynthesis of first generations of stars. A remarkable property
of these stars is the large excess of carbon with respect to iron, for
which several nucleosynthesis models have been proposed. In this
context, our studies for carbon-enhanced metal-poor (CEMP) stars are
reviewed. While the triple-alpha process in the evolved
intermediate-mass stars (AGB stars) is suggested as the origin of
carbon in a majority of CEMP stars, remaining stars are not well
explained by this process, in particular in the lowest metallicity
range. Detailed chemical compositions suggest that the origin of
carbon in at least some of these stars is the so-called "faint
supernovae" producing little amount of iron, which is also applicable
to the HMP stars.