  Some conceptual issues concerning general invariant theories, with special
emphasis on general relativity, are analyzed. The common assertion that
observables must be required to be gauge invariant is examined in the light of
the role played by a system of observers. Some features of the reduction of the
gauge group are discussed, including the fact that in the process of a partial
gauge fixing the reduction at the level of the gauge group and the reduction at
the level of the variational principle do not commute. Distinctions between the
mathematical and the physical concept of gauge symmetry are discussed and
illustrated with examples. The limit from general relativity to special
relativity is considered as an example of a gauge group reduction that is
allowed in some specific physical circumstances. Whether and when the
Poincar\'e group must be considered as a residual gauge group will come out as
a result of our analysis, that applies, in particular, to asymptotically flat
spaces.
