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One of the challenges grid technology faces today is the adoption in other domains than scientific computing, where it originated. However, in order to be usable and useful into other domains, it needs to be adapted and extended to fit the needs of the domain and yet maintains the standards defined by OGSA (I. Forster et al., 20020) and WSRF (2004). We focus on the domain of enterprise grids (S. Robinson, 2004), which are comprised of the interconnected data centers as they exist in commercial enterprises forming large pools of geographically distributed IT resources that are shared among numerous IT applications. In this paper, we compare the commonalities and differences between compute grids (I. Foster and C. Kesselman) and enterprise grids. We then introduce the concept of resource topologies which is important for enterprise grids. A design tool is presented for designing resource topologies. In the second part of the paper we introduce the problem of resource composition and present a solution for exploring a space of possible resource compositions for meeting application requirements using a policy-based constraint satisfaction method.