Suppose that X is a real Banach space, K is a nonempty closed convex subset of X and T : $K; ightarrow;K$ is a uniformly continuous ø-hemicontractive operator or a Lipschitz ${phi}-hemicontractive$ operator. In this paper we prove that under certain conditions the three-step iteration methods with errors converge strongly to the unique fixed point of T. Our results extend the corresponding results of Chang [1], Chang et a1. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10], Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu [17].