  The coupled Einstein-Yang-Mills equations on a time dependent axially
symmetric spacetime are investigated, without a priori any conditions on the
gauge field. There is numerical evidence for the existence of a regular
solution with the desired asymptotic features. Just as in the supermassive
abelian counterpart model, the formation of a singularity at finite distance of
the core of the string depends critically on a parameter of the model, i.e.,
the constant value of one of the magnetic components of the YM potentials. The
multiple-scale method could supply decisive answers concerning the stability of
the solution.
