  We address the problem of observables in generally invariant spacetime
theories such as Einstein's general relativity. Using the refined notion of an
event as a ``point-coincidence'' between scalar fields that completely
characterise a spacetime model, we propose a generalisation of the relational
local observables that does not require the existence of four everywhere
invertible scalar fields. The collection of all point-coincidences forms in
generic situations a four-dimensional manifold, that is naturally identified
with the physical spacetime.
