"A hamiltonian approach to lagrangian Noether transformations" It is proven that each lagrangian Noether symmetry --rigid or gauge-- can be easily obtained from a kind of "hamiltonian generator", which is a conserved quantity satisfying a simple condition. This yields a procedure to construct Lagrangian gauge transformations. It is also shown that some regularity conditions are needed in order to assure the existence of hamiltonian gauge generators: we exhibit an example which has no such generators, though Noether gauge transformations can be constructed for it. We apply our method to obtain the covariant gauge transformations of the bosonic string from its hamiltonian constraints.