Local symmetries and the noether identities in the Hamiltonian framework

We study in the Hamiltonian framework the local transformations delta (epsi lon)q(A)(tau) = Sigma ([k])(k=0) partial derivative (k)(tau)epsilon R-a((k) a)A(q(B), (q over dot)(C)) which leave invariant the Lagrangian action: del ta S-epsilon = div. Manifest form of the symmetry and the corresponding Noe ther identities is obtained in the first order formalism as well as in the: Hamiltonian one. The identities have very simple form and interpretation i n the Hamiltonian framework. Part of them allows one to express the symmetr y generators which correspond to the primarily expressible velocities throu gh the remaining one. The other part of the identities allows one to select subsystem of constraints with a special structure from the complete constr aint system. It means, in particular, that the above written symmetry impli es an appearance of the Hamiltonian constraints up to at least ([k] fl) sta ge. It is proven also that the Hamiltonian symmetries can always be present ed in the form of canonical transformation for the phase space variables. T he manifest form of the resulting generating function is obtained.