  We describe symmetry structure of a general singular theory (theory with
constraints in the Hamiltonian formulation), and, in particular, we relate the
structure of gauge transformations with the constraint structure. We show that
any symmetry transformation can be represented as a sum of three kinds of
symmetries: global, gauge, and trivial symmetries. We construct explicitly all
the corresponding conserved charges as decompositions in a special constraint
basis. The global part of a symmetry does not vanish on the extremals, and the
corresponding charge does not vanish on the extremals as well. The gauge part
of a symmetry does not vanish on the extremals, but the gauge charge vanishes
on them. We stress that the gauge charge necessarily contains a part that
vanishes linearly in the first-class constraints and the remaining part of the
gauge charge vanishes quadratically on the extremals. The trivial part of any
symmetry vanishes on the extremals, and the corresponding charge vanishes
quadratically on the extremals.
