  We discuss the issue of observables in general-relativistic perturbation
theory, adopting the view that any observable in general relativity is
represented by a scalar field on spacetime. In the context of perturbation
theory, an observable is therefore a scalar field on the perturbed spacetime,
and as such is gauge invariant in an exact sense (to all orders), as one would
expect. However, perturbations are usually represented by fields on the
background spacetime, and expanded at different orders into contributions that
may or may not be gauge independent. We show that perturbations of scalar
quantities are observable if they are first order gauge-invariant, even if they
are gauge dependent at higher order. Gauge invariance to first order plays
therefore an important conceptual role in the theory, for it selects the
perturbations with direct physical meaning from those having only a
mathematical status. The so-called ``gauge problem'', and the relationship
between measured fluctuations and gauge dependent perturbations that are
computed in the theory are also clarified.
