We first prove a resul on the asymptotic behavior of almost-orbits of nonexpansive semigroups without convexity in a Hilbert space. This is a generalization of results of Rodé [7] and Takahashi [10]. Further we prove a fixed point theorem for Lipschitzian semigroups without convexity. This is a generalization of results of Lau [3], Takahashi [8], [10] and Ishihara [2].
