  Convergence to stationary solutions in fully nonlinear parabolic systems with
general nonlinear boundary conditions is shown in situations where the set of
stationary solutions creates a $C^2$-manifold of finite dimension which is
normally stable. We apply the parabolic H\"older setting which allows to deal
with nonlocal terms including highest order point evaluation. In this direction
some theorems concerning the linearized systems is also extended. As an
application of our main result we prove that the lens-shaped networks generated
by circular arcs are stable under the surface diffusion flow.
