We consider the problem of building a P2P-based search engine for massive document collections. We describe a prototype system called ODISSEA (Open DIStributed Search Engine Architecture) that is currently under development in our group. ODISSEA provides a highly distributed global indexing and query execution service that can be used for content residing inside or outside of a P2P network. ODISSEA is different from many other approaches to P2P search in that it assumes a two-tier search engine architecture and a global index structure distributed over the network. We give an overview of the proposed system and discuss the basic design choices. Our main focus is on efficient query execution, and we discuss how recent work on top? queries in the database community can be applied in a highly distributed environment. We also give preliminary simulation results on a real search engine log and a terabyte web collection that indicate good scalability for our approach.