  We derive for generally covariant theories the generic dependency of
observables on the original fields, corresponding to coordinate-dependent gauge
fixings. This gauge choice is equivalent to a choice of intrinsically defined
coordinates accomplished with the aid of spacetime scalar fields. With our
approach we make full contact with, and give a new perspective to, the
"evolving constants of motion" program. We are able to directly derive generic
properties of observables, especially their dynamics and their Poisson algebra
in terms of Dirac brackets, extending earlier results in the literature. We
also give a new interpretation of the observables as limits of canonical maps.
