  Evolution of systems in which Hamiltonians are generators of gauge
transformations is a notion that requires more structure than the canonical
theory provides. We identify and study this additional structure in the
framework of relational observables ("partial observables"). We formulate
necessary and sufficient conditions for the resulting evolution in the physical
phase space to be a symplectomorphism. We give examples which satisfy those
conditions and examples which do not. We point out that several classic
positions in the literature on relational observables contain an incomplete
approach to the issue of evolution and false statements. Our work provides
useful clarification and opens the door to studying correctly formulated
definitions.
