  We investigate the space-time structure of the classical gluon field produced
in an ultrarelativistic collision between color charges. The classical solution
which was computed previously in a perturbative approach is shown to become
unstable on account of the non-Abelian self-interaction neglected in the
perturbative solution scheme. The time scale for growth of the instabilities is
found to be of the order of the distance between the colliding color charges.
We argue that these instabilities will eventually lead to thermalization of
gluons produced in an ultrarelativistic collision between heavy nuclei. The
rate of thermalization is estimated to be of order $g^2 \mu$, where $g$ is the
strong coupling constant and $\mu^2$ the transverse color charge density of an
ultrarelativistic nucleus.
