Please note special time.   In this talk we will present a Hamiltonian Formulation of the water waves problem with vorticity and we will study the long wave limit. In the shallow-water regime (long waves) the characteristic lenght of the horizontal motion is assumed much larger than the depth. Because this difference in the scales, the water waves equation can be simplified. In the first part of the presentation we will justify the existence of this limit in presence of vorticity and in the second one we will dicuss some properties of the models obtained.