  We study Wave Maps from R^{2+1} to the hyperbolic plane with smooth compactly
supported initial data which are close to smooth spherically symmetric ones
with respect to some H^{1+\mu}, \mu>0. We show that such Wave Maps don't
develop singularities and stay close to the Wave Map extending the spherically
symmetric data with respect to all H^{1+\delta}, \delta<\mu_{0}(\mu). We obtain
a similar result for Wave Maps whose initial data are close to geodesic ones.
This generalizes a theorem of Sideris for this context.
