  Previous analyses on the gauge invariance of the action for a generally
covariant system are generalized. It is shown that if the action principle is
properly improved, there is as much gauge freedom at the endpoints for an
arbitrary gauge system as there is for a system with ``internal'' gauge
symmetries. The key point is to correctly identify the boundary conditions for
the allowed histories and to include the appropriate end-point contribution in
the action. The path integral is then discussed. It is proved that by employing
the improved action, one can use time-independent canonical gauges even in the
case of generally covariant theories. From the point of view of the action and
the path integral, there is thus no conceptual difference between general
covariance and ``ordinary gauge invariance''. The discussion is illustrated in
the case of the point particle, for which various canonical gauges are
considered.
