Currently, Grid technologies are widely used in largescale scientific applications. Grids support stateful interactions with explicit exposure of state information across the boundaries of a service. In this paper, we present a stateful Web service architecture that provides efficient sharing of a service instance between heterogeneous service requesters with monitoring of the interactions. We describe how we compose the state information based on the formalized sequence of the interactions. We also describe how the shared service instance is managed, and interacted with, through standard Web services interfaces. We analyze the performance of our approach in a large-scale scientific Grid application.