The evolution of physical and gauge degrees of freedom in the Einstein and
Yang-Mills theories are separated in a gauge-invariant manner. We show that the
equations of motion of these theories can always be written in
flux-conservative first-order symmetric hyperbolic form. This dynamical form is
ideal for global analysis, analytic approximation methods such as
gauge-invariant perturbation theory, and numerical solution.Comment: 12 pages, revtex3.0, no figure