$N$ values should be indicative for the way in which the evolution of massive first stars is affected by the mass loss.

To facilitate a comparison with models without mass loss the initial conditions for the models presented here have been chosen the same like in Paper I.

The chemical composition corresponding to galactic lower metallicity stars is ($X,Z=0.765,10^{-6}$), and for pregalactic ones ($X,Z=0.765,10^{-9}$) by using a value $Y=0.235$ as a primordial helium value. The initial stellar masses have been chosen $100$, $120$, $150$, $200$, and $250\,M_{\odot}$. For the mass loss parameter we have used the values $N=50$ and $100$.

Properties of the models {#properties}
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The evolutionary models presented here predict the effective temperature, luminosity and other physical variables and quantities for very massive Population III mass losing stars during the hydrogen and helium burning phases, for the initial masses and mass loss parameters chosen.

Figures \[bar\_fig1\] to \[bar\_fig4\] show some physical variables during the hydrogen and helium burning for pregalactic stars with masses $100$, $120$, $150$, $200$, and $250\,M_{\odot}$, metallicity $Z=10^{-9}$ and mass loss parameter $N=100$.

![Central density for $100\,M_\odot$ (solid line), $120\,M_\odot$ (dash-dot-dot-dot-dash), $150\,M_\odot$ (dashes), $200\,M_\odot$ (dash-dot-dash) and $250\,M_\odot$ (dots) pregalactic Population III stars with metallicity $Z=10^{-9}$ 