do not experience the AGB phase.

Figures  \[bar\_fig11\] to  \[bar\_fig14\] show evolutionary tracks in the HR diagram for $100$, $120$, $150$, $200$ and $250\,M_{\odot}$, for mass loss parameters $N=50$ and $N=100$, corresponding to galactic and pregalactic Population III stars with metallicity $Z=10^{-6}$ and $Z=10^{-9}$, respectively.

Discussion
==========

Population III stars are defined as all metal deficient stars which share the common peculiarity of experiencing self-production of C sometimes during their H-burning evolution [@Castellani2000]. That is, these stars may build-up a small fraction of C nuclei ($Z_{\rm
C}\sim 10^{-10}$) via the triple-$\alpha$ reactions during the pre-main sequence [@Cassisi1993].

Then, these stars produce their nuclear energy during the H-burning phase from a combination of the proton-proton (pp) chain and the CNO-cycle with the small amount of C previously built. To provide the necessary luminosity, the star has to reach very high central temperatures $T_{\rm c}\sim 10^{8}$ K for the simultaneous occurrence of the helium burning via the $3\alpha$ process. This burning produces certain amount of heavy elements to follow efficiently the CNO-cycle.

In our models, the lower is the metallicity, the sooner is activated the triple-$\alpha$ reaction during the main-sequence. Lower-metallicity pregalactic stars without mass loss produce higher nuclear energy via the 