We present evolutionary models of zero-metallicity very massive objects, with initial masses in the range 120 Msun -- 1000 Msun, covering their quiescent evolution up to central carbon ignition. In the attempt of exploring the possible occurrence of mass loss by stellar winds, calculations are carried out with recently-developed formalisms for the mass-loss rates driven by radiation pressure (Kudritzki 2002) and stellar rotation (Maeder & Meynet 2000).The study completes the previous analysis by Marigo et al. (2001) on the constant-mass evolution of primordial stars. Our results indicate that radiation pressure (assuming a minimum metallicity Z = 10^{-4} Zsun)is not an efficient driving force of mass loss, except for very massive stars with M >= 750 Msun. On the other hand, stellar rotation might play a crucial role in triggering powerful stellar winds, once the (Omega-Gamma)-limit is approached. However, this critical condition of intense mass loss can be maintained just for short, as the loss of angular momentum due to mass ejection quickly leads to the spinning down of the star. As by-product to the present work, the wind chemical yields from massive zero-metallicity stars are presented. The helium and metal enrichments, and the resulting Delta(Y)/Delta(Z) ratio are briefly discussed.
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