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As Grid technology is expanding from scientific computing to business applications, transactional workflow management emerges as one of the most important services for Grids. The ShanghaiGrid project launched in Shanghai, China implemented a basic workflow service without the reliability support. In this paper , we propose a transactional Grid workflow service (GridTW), providing a reliable and automatic workflow management for the ShanghaiGrid as well as other Grid workflow applications. This paper focuses on how to manage Grid transactions and combine transaction management with the workflow service. We present an automatic compensation based coordination algorithm with which the GridTW guarantees the reliability of Grid workflows. An important feature of our algorithm is that it can adapt to the dynamics Grid applications by the event- and condition-driven mechanism, and allows users to select execution results from committed subtransactions.