The time complexity of wait-free algorithms in “normal” executions, where no failures occur and processes operate at approximately the same speed, is considered. A lower bound of log n on the time complexity of any wait-free algorithm that achieves approximate agreement among n processes is proved. In contrast, there exists a non-wait-free algorithm that solves this problem in constant time. This implies an Ω(log n ) time separation between the wait-free and non-wait-free computation models. On the positive side, we present an O(log n ) time wait-free approximate agreement algorithm; the complexity of this algorithm is within a small constant of the lower bound.