In this paper we establish three results on fixed points of semigroups of Lipschitzian mappings. The first one generalizes Lifschitz’s fixed point theorem for uniformly Lipschitzian mappings in metric spaces. The second one generalizes Kirk’s fixed point theorem for mappings of asymptotically nonexpansive type. The last one generalizes Lim-Xu’s fixed point theorem for uniformly Lipschitzian mappings satisfying the Casini-Maluta condition.