  We study the perturbations on both "radial" and "angular" components of the
quintessence with an internal abelian and non-abelian symmetry. The properties
of the perturbation on the "radial" component depend on the specific potential
of the model and is similiar for both abelian and non-abelian case. We show
that the consine-type potential is very interesting for the O(\textit{N})
quintessence model and also give a critical condition of instability for the
potential. While the properties of perturbations on "angular" components depend
on whether the internal symmetry is abelian or non-abelian, which we have
discussed respectively. In the non-abelian case, the fluctuation of the
"angular" component will increase rapidly with time while in the abelian case
it will not.
