This thesis work studies a special class of semigroups that satisfy the Lipschitz's_x000D_ condition. They are called semigroups of Lipschitz operators. Here, it is studied_x000D_ some properties of this class of semigroups and the important part is focused in the_x000D_ characterization of its generator._x000D_ The problem of characterizing an operator A as a generator of this class of_x000D_ semigroups is closely related to the Cauchy problem for A :_x000D_ u0(t) = Au(t) for t 0 and u(0) = x_x000D_ where X is a Banach space, A : X ! X is a continuous operator and u : [0;1) ! X_x000D_ an unknown function which is di erentiable in R+. To success, the operator A it is_x000D_ assumed to be continuous from a closed subset D of a real Banach space X satisfying_x000D_ a subtangential condition and a dissipative condition and supported by a functional_x000D_ V that have interesting properties