Within computational grids, some services (software components, linear algebra libraries, etc.) are made available by some servers to some clients. In spite of the growing popularity of such grids, the service discovery, although efficient in many cases, does not reach several requirements. Among them, the flexibility of the discovery and its efficiency on wide-area dynamic platforms are two major issues. Therefore, it becomes crucial to propose new tools coping with such platforms. Emerging peer-to-peer technologies provide algorithms allowing the distribution and the retrieval of data items while addressing the dynamicity of the underlying network. We study in this paper the service discovery in a pure peer-to-peer environment. We describe a new trie-based approach for the service discovery that supports range queries and automatic completion of partial search strings, while providing fault-tolerance, and partially taking into account the topology of the underlying network. We validate this approach both by analysis and simulation. Traditional metrics considered in peer-to-peer systems exhibits interesting complexities within our architecture. The analysis' results are confirmed by some simulation experiments run using several grid's data sets.