As the size of today's grid computing platforms increases, the need for self-organization and dynamic reconfiguration becomes more and more important. In this context, the convergence of grid computing and peer-to-peer (P2P) computing seems natural. However, grid infrastructures are generally available as a hierarchical federation of SAN-based clusters interconnected by high-bandwidth WANs. In contrast, P2P systems usually run on the Internet, on top of random, generally flat network topologies. This difference may lead to the legitimate question of how adequate are the P2P communication mechanisms on hierarchical grid infrastructures. Answering this question is important, since it is essential to efficiently exploit the particular features of grid networking topologies in order to meet the constraints of scientific applications. This paper evaluates the communication performance of the JXTA P2P platform over high-performance SANs and WANs, for both J2SE and C bindings. We discuss these results, then we propose and evaluate several techniques able to improve the JXTA's performance on such grid networking infrastructures.