Features of the P2P model, such as scalability and volatility tolerance, have motivated its use in distributed systems. Several generic P2P libraries have been proposed for building distributed applications. However, very few experimental evaluations of these frameworks have been conducted, especially at large scales. Such experimental analyses are important, since they can help system designers to optimize P2P protocols and better understand the benefits of the P2P model. This is particularly important when the P2P model is applied to special use cases, such as grid computing. This paper focuses on the scalability of two main protocols proposed by the JXTA P2P platform. First, we provide a detailed description of the underlying mechanisms used by JXTA to manage its overlay and propagate messages over it: the rendezvous protocol. Second, we describe the discovery protocol used to find resources inside a JXTA network. We then report a detailed, large-scale, multi-site experimental evaluation of these protocols, using the nine clusters of the French Grid'5000 testbed.