  The stability of metal-free very massive stars ($Z$ = 0; $M = 120 - 500
\msol$) is analyzed and compared with metal-enriched stars. Such zero-metal
stars are unstable to nuclear-powered radial pulsations on the main sequence,
but the growth time scale for these instabilities is much longer than for their
metal-rich counterparts. Since they stabilize quickly after evolving off the
ZAMS, the pulsation may not have sufficient time to drive appreciable mass loss
in Z = 0 stars. For reasonable assumptions regarding the efficiency of
converting pulsational energy into mass loss, we find that, even for the larger
masses considered, the star may die without losing a large fraction of its
mass. We find a transition between the $\epsilon$- and $\kappa$-mechanisms for
pulsational instability at $Z\sim 2\E{-4} - 2\E{-3}$. For the most metal-rich
stars, the $\kappa$-mechanism yields much shorter $e$-folding times, indicating
the presence of a strong instability. We thus stress the fundamental difference
of the stability and late stages of evolution between very massive stars born
in the early universe and those that might be born today.
