  We consider gauge theories from the free evolution point of view, in which
initial data satisfying constraints of a theory are given. Because the
constraints are compatible with the field equations they remain so. We study a
model constrained Hamiltonian theory and identify a particular structure in the
equations of motion which we call the standard gauge freedom. The pure gauge
subsystem of this model theory is identified and the manner in which the gauge
variables couple to the field equations is presented. We demonstrate that the
set of gauge choices that can be coupled to the field equations to obtain a,
properly defined, wave-like formulation is exactly the set of wave-like pure
gauges. Consequently we analyze a parametrized family of formulations of
general relativity. The generalization of the harmonic gauge formulation to a
five parameter family of gauge conditions is obtained.
