  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.
