Simple Temporal Networks (STNs) have proved useful in applications that involve metric time. However, many applications involve events whose timing is uncertain in the sense that it is not controlled by the execution agent. In this paper we consider execution algorithms for temporal networks with events of uncertain duration. We present two such algorithms. The first retains maximum flexibility, but requires potentially costly updates during execution. The second surrenders some flexibility in order to obtain a fast execution comparable to that available for ordinary STNs.