Symmetry generators in singular theories

It is proved that in the singular nondegenerate theories any symmetry of the lagrangian under non-point transformations of lagrangian variables with the open (in the general case) algebra in the hamiltonian approach generates corresponding transformations of canonical variables, the generator of which is the Noether charge with respect to the Dirac brackets. On the surface of all constraints these transformations leave the hamiltonian invariant and the algebra of the Noether charges is closed. As a consequence, it is shown that the nilpotent BRST charge operator always exists in gauge theories of the general form (if possible anomalies are not taken into account).